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Talk:Von Neumann universe

What about urelements?
Does that mean that every element of every set is always a set itself, too? Are sets like 'the set of current or former U.S. Presidents', whose elements aren't sets, disallowed? If so, what the f*** does it mean "The band Metallica has four members"? The most obvious answer is that the sets {James Hetfield; Lars Ulrich; Kirk Hammett; Robert Trujillo} and 4 = {0; 1; 2; 3} = {{}; – ; {{};  – }; {{};  – ; {{};  – }}} are equipotent. But here I learn that the former is not a set, as its elements aren't themselves sets, so what does it mean?

 * In the Von Neumann universe, if a set has any elements at all, then the elements must themselves be sets. "Sets" containing elements which are not sets are not allowed in this universe by definition.  What you are probably looking for are universes with urelements, which allow sets containing members that are not themselves sets.  - Gauge 05:46, 24 Jan 2005 (UTC)

Assume ZF- with the necessary modifications to allow urelements. Following the links between transitive sets, von Neumann universe and well-founded sets it seems that well-founded sets can have urelements in their transitive closure. However, it is not clear whether von Neumann universe
 * 1. is the class of all well-founded sets whose transitive closures do not contain urelements (so that it is the union of all stages in the von Neumann hierarcy.)
 * 2. is the class of all well-founded sets, even if their transitive closures contain urelements (this seems to be the most honest interpretation of the introduction of this article.)
 * 3. is the class of all well-founded sets and all urelements (so that only ill-founded sets are excluded.)

I would be grateful for a clarification of this matter. Lapasotka (talk) 20:37, 17 March 2011 (UTC)
 * It's your number 1. --Trovatore (talk) 21:05, 17 March 2011 (UTC)

Thank you for the quick response! I added this important piece of information into the definition. Lapasotka (talk) 21:31, 17 March 2011 (UTC)

The point is to see what modifications are necessary to add urelements. You could define urelements as sets with no members. Then you must not only drop the axom of Foundation but also change the axiom of extensionality since all urelements have the same members (i.e. none) yet they are distinct. Then you are not in Zermelo set theory at all and you will have to change the definition of the von Neumann universe accordingly---by excluding urelements. Or you could say each urelement is its own sole member, and keep all the axioms of Zermelo Fraenkel except Foundation. Then you can keep the usual definition of the von Neumann universe since these urelements are plainly not well-founded sets.Colin McLarty (talk) 13:35, 11 April 2011 (UTC)

What is Zermelo Fraenkel good for, anyway? Just about everything in any useful form of mathematics is built from urelements. Even the ZF "interpretation" of positive integers is useless, because there are many contexts in which sets of numbers are considered where the "license to reduce" e.g., {0; 1; 2; 3} to 4 doesn't make sense.

198.228.228.153 (talk) 13:14, 29 June 2014 (UTC)Collin237

 * To 198.228.228.153: This is not a problem which exclusively affects ZFC. In most mathematical models of physical systems, the meaning of an element of the model depends on its context, that is, on how it is used in the interpretation of the model — which variable is assigned that element as its value. Whether an element is interpreted as a single integer or as a set of integers depends on the meaning attached to the variable which is assigned that value. JRSpriggs (talk) 05:46, 30 June 2014 (UTC)

The role of ZF and the von Neumann universe in mathematics
To 198.228.228.153: It seems to me that ZF set theory is only a testing ground for mathematical theories. If you can define a model for a theory within ZF, you get all the advantages of the last 100 years' research into consistency, completeness, independence, and so forth. ZF has two big advantages. It has been very well researched, and it is capable of providing models for most mathematical theories. It's solid and it's big. If you can build a model for a theory inside ZF, it's probably as self-consistent and "valid" as you can get at this point in history.

When you have demonstrated that you can build a model for a theory within ZF, you can throw away that interpretation and return to the theory without any particular ZF-based model. For example, you might first build a model for the non-negative integers as 0=∅, 1={∅}, and so forth. In this framework, you can validate your axioms, and then you can just forget the particular representation. Similarly, one represents the real numbers as Cauchy sequences or Dedekind cuts to verify that it's all self-consistent and has the right sorts of properties. Then you throw away the representation when it has served its validation purpose.

If you don't believe that the representation is thrown away, ask 10 typical mathematicians if they believe that the propositions $$1\in2$$, $$1\subsetneq2$$, $$1\cup3=3$$, and $$\cap\, 9=0$$ are true? Chances are that 9 out of 10 of them won't think these statements have any meaning at all. That's because most mathematicians are not interested in ZF models. They know that someone has validated the theories they use, and they just get on with their mathematical lives. Similarly, no one really believes that the number $$\pi$$ is an equivalence class of Cauchy sequences of rational numbers.

The original plan of Peano, Frege, Whitehead and Russell, Hilbert, and others, was to show that mathematics can be modelled within some kind of axiomatic system where consistency can be guaranteed in some way. That plan didn't 100% succeed, but a huge amount of clarity was brought to the issue during the attempt. Some disturbing surprises turned up too, but overall, ZF does seem fairly solid, and it has survived for 100 years, roughly speaking. So it's probably okay. And Gödel showed that AC and GCH are consistent with ZF, and Paul Cohen showed that AC and GCH are independent of ZF. Since 1963, the most important questions have been resolved to most people's satisfaction. The remaining little bits and pieces of the picture are still studied in model theory, but all in all, ZF (with or without AC and/or GCH etc.) looks like it's safe to use. Most importantly, it's a framework where you can define models for theories, and can be fairly confident that if your theory can be embedded/immersed/interpreted in ZF set theory (e.g. in the von Neumann universe), then probably your theory has no consistency problems, assuming that the interpretation map from the theory to the model is validly defined.

In other words, what I'm trying to say is that mathematics does not reside inside ZF. So the atoms don't matter. All that matters is whether you can find a map of some kind from the objects of a theory into ZF. It doesn't matter if a potato is modelled as the set ω and a tomato as the set ω × ω. If the theory is valid when mapped into ZF, you've got the benefit of some kind of standard validation. It's a kind of benchmark which everybody feels they understand well enough. And if ZF does have serious problems which are not yet discovered, we're all in trouble. You'll probably get a prize for discovering any contradictions in ZF. So it's win-win. Either ZF is safe to use, or you get fame and a big prize.

Conclusion: ZF is just a testing ground for theories. Mathematics doesn't reside inside ZF. --Alan U. Kennington (talk) 13:41, 30 June 2014 (UTC)

Define rank
The page "rank (set theory)" redirects to this page. Therefore, this page should define rank without using the word rank in the definition. For example:
 * "The rank of a well-founded set is defined inductively as the smallest ordinal number greater than the ranks of all members of the set."

This defines rank as a number greater than other ranks. If a person is looking for the definition of a rank, this circular dependency will keep them from finding it. -- k a i n a w ™ 19:22, 2 September 2011 (UTC)
 * The definition is actually correct; the circularity is apparent rather than real. For example the empty set has no members, so every ordinal is greater than the ranks of all members of the empty set.  So the rank of the empty set is the least ordinal, period, which is zero.  You proceed from there.
 * Just the same, I agree that it's not too friendly to make the reader work through that problem, and it's also not the most useful definition in practice. I propose replacing it with something like "the rank of x is the least ordinal α such that $$x\in V_{\alpha+1}$$".  --Trovatore (talk) 23:23, 2 September 2011 (UTC)
 * The last sentence in the Von Neumann universe section says "The rank of a set S is the smallest α such that $$S \subseteq V_\alpha \,.$$". If you ignore the first sentence and a half of that section, it gives a non-circular definition. JRSpriggs (talk) 03:18, 3 September 2011 (UTC)
 * Right, and for that matter the apparently circular definition is not actually circular anyway. Just the same, I agree with Kainaw that it's a problem.  I'm not sure of the best fix; it probably requires rewording the lead entirely.
 * I would prefer that the lead be changed to emphasize the iterative, rather than recursive, nature of the hierarchy. I know that's not entirely non-controversial; fans of John Conway are likely to feel otherwise.  However I do feel it's more reflective of the way set theorists usually conceive of these things. --Trovatore (talk) 03:44, 3 September 2011 (UTC)

Could this image be used as a example?
Isn't von Neumann universe some sort of bounding volume hierarchy? --Pasixxxx (talk) 18:19, 3 December 2011 (UTC)

 * No. JRSpriggs (talk) 00:52, 5 December 2011 (UTC)

V and ZFC
I am a little confused at the momemt, and it's sometimes embarrassing to reveal how confused you really are. However, reading the section "Philosofical Perspectives" made me feel a little better. Pretty much everyone is confused. At least, not everyone agrees with everybody else. Good!

I initially wrote a longer post, but decided not to actually post it to save me some of the embarrassment. Basically, I would like to see a longer article. As it stands it's pretty much like a good riddle. It is possible, but pretty time consuming, to find the correct answers.

Here is one "anwer" that I now formulate as a question: Could V in some sense be called the intended model for ZFC? If so, in which sense?

It's hard to think of elements of V that aren't sets (according to ZFC) and, vice versa, permissible sets (in ZFC) that aren't in V. Quote from the article: "In ZFC every set is in V." I think so too, but this isn't obvious at all. But elements of V seem all to be valid ZFC sets by construction. Things like real numbers can be built from the natural numbers. [I am thinking reals as equivalence classes of Cauchy sequences of rational numbers here.] They ought to appear pretty early on in the hierarchy, but when exactly? YohanN7 (talk) 18:48, 4 May 2012 (UTC)
 * Yes, V is the "intended model" of ZFC, with the only caveat being that (from a realist perspective) V cannot be a completed totality, an actual individual object (if it were, it would have to be a set). Therefore the statement "V is the intended model" has to be understood as shorthand for a longer-winded claim, one that would describe the intended interpretation of statements in the language of ZFC, with quantifiers ranging over objects that satisfy "I am in V" as a predicate. --Trovatore (talk) 22:29, 4 May 2012 (UTC)
 * Ok. Quote from the article: If κ is an inaccessible cardinal, then Vκ is a model of Zermelo-Fraenkel set theory (ZFC). Here Vκ is a set. In order to prove that it is a model of ZFC, one would still have to produce that longer-winded claim describing the interpretation of ZFC statements? Then one goes about to show that every axiom of ZFC is true in Vκ. Is that the order of buisiness?

 * Example. The axiom of power set holds in Vκ. If $$S \in V_{\kappa}$$ then $$rank(S)=\lambda < \kappa$$. The power set will have rank $$\lambda + 1 < \kappa$$. (Hm. For this axiom to hold it seems to suffice that $$\kappa$$ is a limit ordinal.)

 * Would the fact that V is a class and Vκ a set make a substantial difference on the practical level?

 * I'd still like a longer article since V seems to be very important (= used in many contexts). YohanN7 (talk) 11:03, 5 May 2012 (UTC)

I had a look at L. That article parallels a little bit what I'd like to see here. There are things in the article universe too that could well be here. Especially that one can use the axiom of regularity to show that (ZFC) sets not in V don't exist. Also, we cannot actually prove that the axiom of choice holds in V (without actually assuming it), can we? So saying that V is a model of ZFC is incorrect strictly speaking. But V can still be "the intended model" of ZFC as V very well might be a model of ZFC, and a very nice model at that. It is a model of ZF according to the article about L. Do I make sense? YohanN7 (talk) 12:41, 5 May 2012 (UTC)

 * If κ is a limit ordinal greater than ω, then Vκ will satisfy all the axioms of ZFC except possibly some instances of the axiom schema of replacement.
 * Given a set S and a relation E⊆S×S, then the statement that (S,E) is a model which satisfies a sentence φ (in the language of set theory) can be encoded in set theory as a predicate with two free variables (one for the model and one for the sentence). Thus it is possible to encode statements and arguments about ZFC (its meta-theory) as statements and deductions within ZFC insofaras they apply to that particular model. JRSpriggs (talk) 20:55, 6 May 2012 (UTC)

Zermelo was the true author of the so-called von Neumann universe
Zermelo was the real author of the so-called von Neumann universe. See Gregory H. Moore, "Zermelo's axiom of choice", Dover Publications, 1982, 2013, pages 270, 279. See also Ernst Zermelo, "Über Grenzzahlen und Mengenbereiche: Neue Untersuchungen über die Grundlagen der Mengenlehre", Fundamenta Mathematicae, 16 (1930) pages 36–40. Would anyone like to add a note to the wiki page to explain that the von Neumann universe was first published by Zermelo? I have been reading the relevant articles by von Neumann himself in the 1920s. Those articles obviously mention the von Neumann construction for the ordinal numbers, which he did in fact first publish, but there is no sign of the so-called von Neumann universe in his papers. The closest thing to the von Neumann universe published by von Neumann himself is in the 1928 article "Die Axiomatisierung der Mengenlehre", Math. Zeit. 27 (1928) pages 235–237, but that is a model which looks very much like the Gödel style of prime-number model, not at all like the von Neumann universe. Alan U. Kennington (talk) 14:11, 6 August 2013 (UTC)
 * So apparently von Neumann did not develop the VNU whereas Zermelo did. Did anyone other than Moore notice this? Tkuvho (talk) 14:21, 6 August 2013 (UTC)

Well, I noticed it when I read through all of the articles where von Neumann could have presented the von Neumann universe in the 1920s. I could find no sign of it. And then finally, while reading through my books on the subject, I noticed that Moore said this on page 270 of the above-mentioned book.
 * Von Neumann obtained his inner model Π as the image of a function ψ defined by transfinite recursion on the class of all ordinals, but did not use the cumulative type hierarchy often attributed to him.

By "cumulative type hierarchy", Moore means of course the von Neumann universe. Moore gives the reference von Neumann 1929, pages 236–238, for the inner model Π. ("Über eine Widerspruchfreiheitsfrage in der axiomatischen Mengenlehre", J. Reine Ang. Math 160 (1929) 227–241. I've just skimmed through this article and saw no sign of the von Neumann universe at all. But it is definitely in the 1930 Zermelo paper as Moore indicates.) Moore says on page 270:
 * To obtain these theorems, Zermelo introduced what is now called the cumulative type hierarchy for set theory.

This is the Zermlo paper which I referred to above, which does definitely present the so-called von Neumann universe. Alan U. Kennington (talk) 15:47, 6 August 2013 (UTC) Alan U. Kennington (talk) 16:11, 6 August 2013 (UTC)

Of course, the Neumann sources cited in the article do not contain the hierarchy, but another source does: John von Neumann: ‚‚Über eine Widerspruchsfreiheitsfrage in der axiomatischen Mengenlehre‘‘, 1928, in: ‚‚Journal für die reine und angewandte Mathematik‘‘ 160 (1929) 227–241. There p. 236f the cumulative hierarchy (nameless). Therefore Neumann is the true author and not Zermelo. Please correct! Wilfried Neumaier (talk) 18:44, 27 December 2022 (UTC)

Redirect from "V-Hierarchy"
This needs a redirect from "V-Hierarchy". I couldn't find it on my own without that.--208.72.139.94 (talk) 04:46, 23 February 2014 (UTC)
 * Well, you're welcome to create it if you like. You might have to register an account to do it.  You probably should also do a little searching to see if there's an alternative meaning for the term, so as not to send people to the wrong place.  --Trovatore (talk) 07:11, 23 February 2014 (UTC)

Philosophical perspectives
The section "Philosophical perspectives" is marked as not containing any references. Well, I just tried to think of where I might find supporting references amongst my collection of 45 books on set theory and foundations of mathematics, and it seems to me that none of them will support this kind of philosophical summary. In fact, I don't think that section makes any sense at all, and it doesn't agree with anything that I have read. It's more like an afternoon tea discussion amongst the undergrads trying to figure out stuff. Sorry to be so negative about it. What I'm trying to say is that either that section should be deleted or improved. I think it's kind of embarrassing as it stands because it says nothing. It will just confuse people who are unfamiliar with the subject and annoy people who understand it.

My personal preference would be to simply delete it. I don't think it can be repaired. Then if someone wants to add something about interpretation as a new section, they could do that by starting with some authoritative literature as a source of references. — Preceding unsigned comment added by Alan U. Kennington (talk • contribs) 02:49, 7 June 2014 (UTC)

Moving the philosophical perspectives to the discussion page
I'm moving the unreferenced philosophical perspectives section to this disccusion/talk page. I think it's dubious that the statements there can be backed up by book references or by wikipedia cross-references. They seem to be someone's personal comments on the possible range of philosophical interpretations, but there is not much value in it as far as I can see. It's not as if V is widely discussed in the literature for its philosophical significance any more than any other model for ZF or ZFC or other theories is discussed. V is just one special case of a model amongst hundreds. (I am retaining the original "unreferenced section" notification.) --Alan U. Kennington (talk) 07:37, 13 June 2014 (UTC)
 * Um. I wrote that, long ago.  I can't really object to your point that it's unreferenced.  However, "just one case of a model" is completely wrong.  V is the intended model.
 * I think everything in the section is accurate, and I think it is valuable. But you're quite correct that it's necessary to source it.  If I get a chance I'll look around. --Trovatore (talk) 10:29, 13 June 2014 (UTC)
 * One good place to look would be Stewart Shapiro's Foundations Without Foundationalism. --Trovatore (talk) 10:31, 13 June 2014 (UTC)
 * Also Penelope Maddy, Believing the Axioms, I. --Trovatore (talk) 10:40, 13 June 2014 (UTC)

Of course, I didn't mean my comments as a criticism of the author of that text. It just bothers me that someone or other slapped an "unreferenced section" label on that section, and I think that this is an obstacle to the article getting a higher ranking. "C class" doesn't sound very good to me, for such a core topic as the von Neumann hierarchy.

I've noticed that in the German version of this page (which is definitely not a translation of the English version), they have an applications section. That might be a good idea for the English-language version. So I added a section for that. I think the philosophical aspects of the interpretation of the von Neumann universe could go in such an "applications" section.

In my opinion, there needs to be some explanation of the status of the model. After all, ZF is often used as a source of models in an "underlying set theory" for more general model theory, particularly for a wide range of independence and relative consistency proofs. Therefore clarification of the status of V is at the core of a lot of model theory. I think this is a strong motivation to provide some philosophical background for V. After all, it seems to be a kind of boot-strap model from which other models are derived. It's a very circular thing, building V within ZF and then claiming that V is a model for ZF. It is this circularity which requires some clarification. It's related, I think, to the fact that Gödel's incompleteness theorem says you can't prove consistency for ZF within ZF (since ZF contains the integers). I think any philosophical commentary should connect the status of V with Gödel's results. --Alan U. Kennington (talk) 10:54, 13 June 2014 (UTC)
 * It appears to be a circularity when you present both views at once, yes. But that's because you're trying to affirm two incompatible views at the same time.  For the formalist, ZF comes first and V follows; for the realist, it's the other way around.  Very roughly speaking.
 * So yes, this does require clarification. That's kind of what I was trying to do in the passage you removed.  You were probably correct to remove it, because of the sourcing issue, but the basic content ought to be restored somehow. --Trovatore (talk) 10:59, 13 June 2014 (UTC)

Agreed. In fact, I think the question of the status of V needs several paragraphs of explanation. So you say, you can resolve the circularity by starting with one or the other as "a-priori", and then the other derives some status from it. This could be explained within the very general context of models for theories though. As you say, it is a question of formalism versus realism. So it really leads into the big questions of the direction mathematical logic took in the 20th century. In my personal opinion, it was the crisis created by Gödel which made everyone realise that Hilbert's program wasn't going to work. And that led to the split between proof theory and model theory. Nowadays, I would say that mathematical logic takes the very cynical view that languages are the primary thing, and theories are completely arbitrary, and models are an afterthought. I take the opposite view. I think that mathematical objects exist in human minds and in the mathematical community. The theories exist only to try to axiomatize and systematize large bodies of objects whose existence is self-evident to mathematicians. As someone once observed, the paradoxes in mathematics never put the brakes on mathematics. They just don't matter because they are in the realm of the theory, which is an imperfect description of the reality. The reality continues to exist when the theory hits a crisis.

In other words, what I'm saying is that any references for this subject could be really references for the general issues of models versus theories. That's just my two cents' worth. I'm not an expert in this area. I just want to understand what it all means! --Alan U. Kennington (talk) 11:11, 13 June 2014 (UTC)

 * The above comments remind me very much of a similar problem with the interpretation of quantum mechanics. Every few years, someone takes a poll of attendees leaving some conference, as to which interpretation they prefer, and, over the course of decades, you can see overwhelming, complete shifts of viewpoints. One also sees large differences between the opinions of the "average practicing physicist" and that subgroup that "bothered to think about the problem in depth", and these two tend to be in diametric opposition.  So the description and determination of the beliefs is a sociological, anthropological problem -- an interesting one, but where things shift around.  Alan Kennington seems to be a platonist, given the remarks above (e.g. "The reality continues to exist when the theory hits a crisis"), but by reading through some of the "13 essays in the philosophy of mathematics" indicates there is much more to it than just that -- platonism itself, the belief in the reality of mathematics, is just another viewpoint, and is hardly an "obviously correct" viewpoint (except to those who believe in it, in which case it appears to be self-evident. How odd...)

 * That said, yes, a good discussion of the different philosophical viewpoints is worthwhile, even if it is unreferenced. If not here, then somewhere? 84.15.181.100 (talk) 08:20, 13 June 2016 (UTC)

Existential status of V
I have added a "stub subsection" for the existential status of V. I think (hopefully) that this is more or less the same as the topic of the "philosophical perspectives" section which I (so rudely) removed. I have tried to add some references for it.

If this new "stub subsection" is unacceptable, please modify or delete it. --Alan U. Kennington (talk) 12:58, 13 June 2014 (UTC)

Philosophical perspectives (moved out of the main page)
There are two approaches to understanding the relationship of the von Neumann universe V to ZFC (along with many variations of each approach, and shadings between them). Roughly, formalists will tend to view V as something that flows from the ZFC axioms (for example, ZFC proves that every set is in V). On the other hand, realists are more likely to see the von Neumann hierarchy as something directly accessible to the intuition, and the axioms of ZFC as propositions for whose truth in V we can give direct intuitive arguments in natural language. A possible middle position is that the mental picture of the von Neumann hierarchy provides the ZFC axioms with a motivation (so that they are not arbitrary), but does not necessarily describe objects with real existence.

Is V really a model for ZFC? Where is C shown to be true?
I am skeptical about the claim that the full von Neumann hierarchy V is a model for ZFC. I think this assertion arises from the confusion regarding the meaning of "Zermelo-Fraenkel set theory". Some people define it as ZF and other define it as ZFC. I know that AC was part of the original set of axioms historically, but that's not the point. The important point is that most authors (and I could give many examples) mean ZF without choice when they say "Zermelo-Fraenkel". But that is not the question I want to discuss here. It is only the background which could lead to a false or misleading assertion here.

If someone could provide a reference where there is a proof that V is a model for ZFC, that would be very useful. The Paul Cohen "Set theory and the continuum hypothesis" book says that V is a ZF model, and on page 88 says that AC and GCH are provable in ZF if you assume V=L. Well, that looks a fairly authoritative statement that the von Neumann universe on its own does not give you AC. At least it is not provable! Smullyan and Fitting, "Set theory and the continuum problem", on page 97, say that V is a model for ZF without any mention of AC. According to Gregory H. Moore, "Zermelo's axiom of choice", page 281, Gödel showed in 1938 that AC is satisfied by VΩ, where Ω is the least strongly inaccessible ordinal. I don't want to do a complete literature search on this. Perhaps the full-time professionals in this area can throw some light on it.

Just to recapitulate, my question is whether it is provable that the complete hierarchy V satisfies AC. If so, could someone provide a reference. If not, I think the wiki page should be modified to say that V is a model for ZF, not for ZFC. --Alan U. Kennington (talk) 03:39, 7 June 2014 (UTC)

 * This whole construction does not make sense unless one assumes some underlying theory of sets. If that theory is ZFC, then Vκ (for κ inaccessible) will be another model of ZFC because the choice function for any set of nonempty sets in Vκ will also be in Vκ. See the beginning of the second paragraph of Inaccessible cardinal for a possibly better wording.
 * If the underlying theory is merely ZF, then one must ask what does "inaccessible cardinal" mean? If it is a strong limit cardinal (among other things), then for all κ < λ, 2κ < λ. If the powerset of any ordinal number below λ can be injected into λ, then the axiom of choice does hold in Vλ. JRSpriggs (talk) 05:24, 7 June 2014 (UTC)

Reading between the lines here, I gather that there is no proof that AC is valid for the full von Neumann hierarchy V. But many sources assert that V is a model for ZF without assuming AC. I don't see that an understanding of inaccessible cardinals is relevant to asserting that V satisfies ZF, with or without AC. I have not seen it written anywhere that the definition of V requires the definition of inaccessible cardinals. When you say "does not make sense", do you mean that V cannot be defined without the axiom of choice. Suppose no one had ever discussed inaccessible cardinals of the axiom of choice ever. Then would V make sense? I think the answer is yes. It seems to me that V is defined to be closed under all of the constructive operations of ZF. The axiom of choice is very definitely not a constructive operation! So how can it be said that AC is required for defining V? I don't think that inaccessible cardinals play any role in the definition of the closure of V under all ZF operations.

I would like to separate out the downstream applications and analysis of V from the definition of it. To me, it seems that AC is not part of the definition. It is either a provable property or it is not. Inaccessible cardinals are likewise attributes of V, not part of the definition. And as far as I can see, AC cannot be proved for the full hierarchy V. Therefore it should not be asserted to be so on the wiki page. If you have a proof of AC for V, I think it should be referenced. If you need extra definitions, like inaccessible cardinals, in order to make the AC assertion, then that is a kind of conditional proof, requiring extra assumptions. Without those extra assumptions, it seems like V is not a ZFC model. --Alan U. Kennington (talk) 05:40, 7 June 2014 (UTC)

To put it another way, is the following statement true?

1. The von Neumann cumulative hierarchy V is a model for ZF. 2. Under certain additional assumptions [... insert assumptions here ...], it can be shown that V is a model for ZFC. --Alan U. Kennington (talk) 06:36, 7 June 2014 (UTC)
 * You can't prove that V satisfies choice without assuming choice. But this is nothing special about choice.  You also can't prove that V satisfies, say, replacement, without assuming replacement. --Trovatore (talk) 21:42, 7 June 2014 (UTC)

Thanks. That sounds like what I suspected. So I'm guessing that if the underlying set theory for defining the cumulative hierarchy V is ZF set theory, then V satisfies ZF (although not provably so within ZF), and if the UST is assumed to be ZFC, one may obtain a cumulative hierarchy V which satisfies ZFC.

So now another question which is directly relevant to the correctness of the article is whether the von Neumann universes defined with ZF and ZFC as the UST are different universes. If so, then I also ask myself what happens with the 158 choice axioms and choice-like principles in the Howard/Rubin book "Consequences of the axioms of choice", pages 91–103, about 80 of which are more or less independent. Since there are so many choices for the axiom of choice, if your UST determines what you get for the minimum cumulative hierachy, that means that the word "the" in the article needs to be replaced with "a". E.g., are the ZF, ZF+AC and ZF+ACω versions of V different?

My personal guess is that there is one and only one minimum cumulative hierarchy of sets (without atoms) which is closed under all of the operations of ZF. My guess is that the various axioms of choice have no influence on the construction at all. And I guess also that since it is not known, and not knowable, whether V satisfies the weakest AC, and the strongest AC, and everything in between, anyone is free to speculate as they wish. And if they speculate that V satisfies the full AC, they get certain consequences, which lead to the towers of metatheorems which I have read some of in the books on model theory. And if they don't speculate about V satisfying any AC axioms at all, they get nothing. And I think that is maybe why people add AC into the UST, namely to generate interesting theorems which are contingent on the ad-hoc assumption that the "construction" V satisfies some kinds of AC conditions.

I conclude from this that the article should be expressed in terms of ZF without AC, because V is really constructed from ZF alone, since AC is in no way a constructive axiom. (Similarly the axiom of regularity plays no concrete role in the construction.) This is not just fairly clear to a non-specialist like me. It also appears in the standard textbooks which I have consulted. I think the addition of C to ZF is perhaps just a habit because so many researchers need it to bootstrap their metatheorems and research. But that is no reason to add it everywhere, like pouring tomato ketchup over everything on the plate. But in my own work, I am trying to determine what can be done with no AC at all. (Yes, I realise that many authors have written extensively on this already.) My thinking is, if AC is superfluous, don't add it. Some foods don't need ketchup!

If I am right about any of this, I think some changes would be beneficial to the article. --Alan U. Kennington (talk) 03:28, 8 June 2014 (UTC)

 * If you are worried about constructiveness, then look at Kripke–Platek set theory. AC is not the only nonconstructive thing in ZFC.
 * The way that you are thinking about this makes no sense — there is at most one V.
 * A formalist would work within some theory of sets and then find that the V constructed using that theory satisfies that theory (duh), except for non-well-founded elements. He could choose to use a different theory, but there would be no question of comparing the Vs of these theories since they do not really exist.
 * A Platonist would believe that the real V already satisfies some theory of sets, and one cannot change that theory, so there are no other Vs to compare with the real one. JRSpriggs (talk) 11:14, 8 June 2014 (UTC)

Many thanks. That confirms my initial tentative understanding of the subject. Now it is no longer so tentative. As far as I can see, there is no possibility of proving that V is a model for ZFC, and the axiom of choice has really very little to do with the definition of V at all. I just personally prefer to see definitions and their properties clearly delineated. The article starts off talking about ZFC, which really is not the right context, I think. It's really a ZF concept which can be studied downstream from the definition within the context of AC questions. Hence I would prefer to see the article steer well clear of AC and the "C" in ZFC until after V has been defined. Then the implications for AC could be gone into.

By the way, I read through the original 1930 German article by Zermelo where von Neumann's cumulative hierarchy for ordinal numbers was first applied to a ZF universe of sets in a published work, and Zermelo explicitly excludes axiom of choice from any role in the definition of the hierarchy. He lays out the ZF axioms one by one, and says that AC is intentionally not one of them! --Alan U. Kennington (talk) 12:40, 8 June 2014 (UTC)
 * I think you're kind of missing the point. V is not a "ZF-concept".  It's a concept that can be directly understood without reference to any formal theory at all.  It's the same thing, whether you then choose to prove theorems about it using ZFC, ZF, Z, KP, ZFC+large cardinals, or what have you.
 * There is no reason to call out AC separately here as though it has some weird status different from those of other ZFC axioms. --Trovatore (talk) 20:20, 9 June 2014 (UTC)

That is in fact what I had assumed for many years until I looked at this wikipedia article. The section "V and set theory" says this:

 * If κ is an inaccessible cardinal, then Vκ is a model of Zermelo-Fraenkel set theory (ZFC) itself, ....

Now I had thought that the very definition of V was that it was the minimum model which is closed under the ZF "constructive axioms", particularly the infinity axiom, the power-set axiom, the union axiom and the replacement axiom, in the same sense that one defines the span of a set of vectors as the intersection of all vectors spaces containing a given set of vectors and closed under vector space operations. Also the same thing for the subgroup generated by a set of elements, and so forth for every algebraic category. So I thought that in the case of set theory, the von Neumann universe was the "span" of the empty set, and with ZFA, you get the span of a set of atoms, and so forth. So then it comes as a surprise that Vκ is a model for ZF, when supposedly Z is the minimum model closed under ZF operations. This is what triggered my fear that maybe when you "construct" V under ZFC assumptions, there could be some magical way that I don't know about whereby now a proper sub-model of V now becomes the minimum model for ZF. This is not just my own personal interest. I am sure that anyone who knows the basic "span" constructions of the algebraic categories would be scratching their heads too. So my question is: How come V is the span of the empty set in ZF theory, and then in ZFC theory, Vκ is the span of the empty set? It is the most basic thing one could ask about the von Neumann universe. Is it really the minimum model for ZF? Or is the minimum dependent on which additional axioms one throws in?

On the subject of minimality, I think one of the other very fundamental questions might ask with a bit of basic background in basic algebra is what is the relation to the constructible universe? It appears on the face of that L is also the minimum model for ZF because it contains the empty set and is closed under all constructive operations of ZF. This question seems to be a bit metaphysical to me because we can't ever "know" what the sets look like inside V ∖ L since they are not constructible. So the existence of sets in V ∖ L is a matter of "Platonic faith" in the same way that the existence of a well-ordering of the real numbers is a matter of faith in V, whereas a well-ordering of the real numbers in L can in principle be written down explicitly. If there is nothing "out there" beyond L, then maybe Lebesgue non-measurable sets don't "exist", for example. Once again, I think these questions are basic, not esoteric.

Q1: If V is the minimum model for ZF, then how come the sub-model Vκ is a model for ZF?

Q2: If V is the minimum model for ZF, then how come L is the minimum model for ZF?

Even someone with basic undergraduate algebra would ask such questions. And I still claim that AC should be introduced in the article after V has been defined. My apologies for persisting with this matter. --Alan U. Kennington (talk) 00:33, 10 June 2014 (UTC)
 * No no no. V is not a minimal model.  It's more like a maximal one.  At every stage, you take all subsets of the previous stage, not just enough to make separation true. --Trovatore (talk) 05:11, 10 June 2014 (UTC)

Okay. So one might think of L as minimal, and V as maximal. Then if AC is assumed to be in force, one can identify a stage Vκ where the transfinite recursion can be safely terminated while still ensuring closure under all ZF operations. I think that makes better sense now. Wouldn't you agree that the addition of some kind of note to this effect would increase the value of the page for the non-specialist reader? I don't want to add anything myself that I'm not rock-solid certain about. (I have only learned about this subject by reading books!) --Alan U. Kennington (talk) 05:46, 10 June 2014 (UTC)

Adequacy of Vω+ω
According to Von Neumann universe, "it is questionable whether such a universe is adequate for all 'ordinary mathematics'". However, from the compactness theorem and downward Löwenheim–Skolem theorem, we know that every consistent theory (which is countable as any actual theory must be) has a countable model. In particular, ZFC itself has countable models even if one adds additional large cardinal axioms (as long as the resulting theory is still consistent). If a model is countable, then one can map its elements injectively into Vω. Any n-ary relation on that base set may be represented by a set of ordered n-tuples of such elements. These n-tuples are also elements of Vω. To represent the whole model itself, one tags the elements of each relation with a symbol representing that relation. A tagged element is just an ordered pair of the symbol and the n-tuple and thus also an element of Vω. Then the set of all such tagged elements (a subset of Vω and thus an element of Vω+1) represents the whole model.

Since all such models are in Vω+1, there is plenty of room in Vω+ω to develop relationships between models and so forth. Thus Vω+ω can only be regarded as "inadequate", if one insists on models which satisfy some conditions from second-order logic or that the "actual" element relation be used in a model of set theory (i.e. a "standard" or "transitive" model) rather than a set of ordered pairs. JRSpriggs (talk) 13:51, 13 June 2014 (UTC)

 * Good! I hope you will add words to that effect to that subsection. Relating V to normal mathematics would make the article much more relevant to non-specialist readers. I have just broken up that subsection into 3 paragraphs which are really about different subjects. I think it's very important that most normal mathematics can be done in Vω+ω. A lot of people would say that Vω+3 is adequate. Maybe the "Applications of V as models for set theories" subsection should be at section level, and then the cases Vω, Vω+ω, etc., could be at subsection level.

--Alan U. Kennington (talk) 14:13, 13 June 2014 (UTC)

ω+ω itself
(However, since the fairly "ordinary" set ω+ω is not itself an element of Vω+ω, it is questionable whether such a universe is adequate for all "ordinary mathematics".) []

That's a concern for "ordinary mathematics" is it? This tacitly assumes the Von Neumann representation of the ordinals. I notice that the article defines

 * $$V_\alpha := \bigcup_{\beta < \alpha} \mathcal{P} (V_\beta)$$

not

 * $$V_\alpha := \bigcup_{\beta \in \alpha} \mathcal{P} (V_\beta)$$

So, this was not even an assumption made in the rest of the article. I don't know that I've ever met any "ordinary mathematicians" but I can only guess they would just use a different representation... --192.75.48.8 (talk) 22:06, 11 March 2015 (UTC)

 * I see that I was reverted but without response. Does the person re-instating the claim think that I am mistaken for thinking ω+ω can be represented? Or does he or she think we "ordinarily" care how objects are represented? Or what? --192.75.48.8 (talk) 14:00, 12 March 2015 (UTC)

 * Since the the statement about "ordinary mathematics" hinges on how "ordinary mathematics" is defined, the qualifying statement is warranted as was explained in the edit summary. For ordinals, $α ∈ β$ if and only if $α < β$ provided that I recall this correctly. Further, I don't think ordinal arithmetic depends on how ordinals are defined. Moreover, their membership in some $V_{α}$ seems to be definition-independent. Maybe ordinal arithmetic is not ordinary mathematics, but then you need to explain that statement. You will invariably then get back to something alike what was in the article before your edits. I have no strong feelings about this. YohanN7 (talk) 14:31, 12 March 2015 (UTC)
 * OK, so 192 is correct on the immediate point of dispute. You can easily represent small ordinals — certainly, all countable ones, and indeed quite a bit more — within Vω+ω, and define arithmetic on them.  It's only if you want them to be von Neumann ordinals that you need to go higher in rank.
 * That said, the "ordinary mathematics" language is still problematic. There are plenty of propositions that are arguably part of ordinary mathematics (say, "every projection of a co-analytic set of reals is Lebesgue measurable") that are not naturally justified by considerations at the level of Vω+ω. --Trovatore (talk) 15:41, 12 March 2015 (UTC)
 * Ok, I stand corrected. But how are countable ordinals represented within Vω+ω, and how is that representation "natural" in any sense? YohanN7 (talk) 16:28, 12 March 2015 (UTC)
 * Well, a countably infinite ordinal is just the order-type of a wellordering of the naturals. Wellorderings of the naturals can be represented as sets of ordered pairs of naturals.  That doesn't give you a canonical representative, because there are different wellorderings with the same order type, but you can take equivalence classes at the price of moving up one rank. --Trovatore (talk) 17:01, 12 March 2015 (UTC)
 * Well, I was only objecting to the particular point, but since you mention it: I think the article's mention of "axiom of replacement" is confused as well. I personally would distinguish between "what is provable in Zermelo set theory" and "what is true in Vω+ω" (as proven by ZFC, or whatever else). What axioms we use to prove things about sets of reals is really not relevant to the question of whether "ordinary mathematics" takes place there or not. For that matter, such axioms may have implications for Vω, but I don't think anybody says Vω is inadequate as a model of finitary mathematics. --GodMadeTheIntegers (talk) 17:21, 12 March 2015 (UTC)

Condensed definition
One reads:

An equivalent definition sets
 * $$V_\alpha := \bigcup_{\beta < \alpha} \mathcal{P} (V_\beta)$$

for each ordinal α, where $$\mathcal{P} (X) \!$$ is the powerset of $$X$$.

Isn't that true only for limit ordinals α ? Should we correct it? --Agatino Catarella (talk) 09:43, 13 August 2023 (UTC)
 * The definition works for successor ordinals as well. The $$\bigcup$$ part turns out to be superfluous, as all the sets from previous stages are also contained in the last stage in the union.
 * I don't personally like this sort of almost "trickological" terseness, but there seem to be people who think that it is not trickological and in fact is informative. We could probably argue about that for days.  If this formulation is in high-quality sources it probably makes sense to include it; otherwise not. --Trovatore (talk) 18:10, 13 August 2023 (UTC)

 * If you use the condensed definition, it becomes easier to prove that the sequence of sets has the desired properties. For example, showing that the sequence is nested follows immediately from big-cup. JRSpriggs (talk) 00:19, 14 August 2023 (UTC)

 * I mean, sure, if you just want to prove that particular fact, maybe you save five seconds. If you actually want to understand what's going on, it seems to me, you still need to understand that the limit and successor cases are different.  In the limit case, nothing new is added that wasn't there before; in the successor case, it is.
 * Put another way, the standard definition takes powersets at successors and unions at limits. The definition under discussion says, ha ha, I can just do both at every step.  At the successor step, the union is redundant, whereas at the limit step, the powersets don't accomplish anything, but I can do it.
 * Anyway that's my aesthetic reaction. If this is done in a high-quality source (Kunen, Jech, Halmos, Enderton, that category) I would withdraw my objection.  If it's present in a lower-quality source, well, we should look at it and discuss. --Trovatore (talk) 16:25, 14 August 2023 (UTC)

 * Thanks a lot everyone for the explanations. I don't like aither too much those definitions that rely on side effects, but that's probably a matter of tastes, indeed. Maybe we could add a word to explain the disappearance of the "limit" word, as I am probably not the first one to wonder. Not sure. --Agatino Catarella (talk) 04:20, 15 August 2023 (UTC)
 * Note that there's a tangentially related discussion at talk:ordinal arithmetic. --Trovatore (talk) 20:37, 15 August 2023 (UTC)
 * This kind of condensed definition seems to be favored by Cohen, at least in the book "Set Theory and the Continuum Hypothesis". The particular definition is in Section II.5 "The Axiom of Regularity", where he first defines the concept of rank in terms of rank functions, and then notes "for future reference that for each ordinal α, we can prove the existence of the set of sets of rank α. Namely, by transfinite induction define $$S(\alpha) = \mathcal{P}(\bigcup_{\beta < \alpha} S(\beta))$$". (Note that the power set operation is on the outside, because "the set of sets of rank ≤α" should be the power set of $$V_\alpha$$.) In Chapter III he defines the constructible universe similarly as "$$M_0 = \varnothing$$ and $$M_\alpha = (\bigcup_{\beta < \alpha} M_\beta)'$$" (where $$x'$$ is his notation for $$\mathrm{Def}(x)$$). Bbbbbbbbba (talk) 06:41, 28 May 2024 (UTC)

title: Talk:Von Neumann universe


text:
Pi backbonding

In chemistry, π backbonding is a π-bonding interaction between a filled (or half filled) orbital of a transition metal atom and a vacant orbital on an adjacent ion or molecule. In this type of interaction, electrons from the metal are used to bond to the ligand, which dissipates excess negative charge and stabilizes the metal. It is common in transition metals with low oxidation states that have ligands such as carbon monoxide, olefins, or phosphines. The ligands involved in π backbonding can be broken into three groups: carbonyls and nitrogen analogs, alkenes and alkynes, and phosphines. Compounds where π backbonding is prominent include Ni(CO)4, Zeise's salt, and molybdenym and iron dinitrogen complexes.

Metal carbonyls, nitrosyls, and isocyanides
The electrons are partially transferred from a d-orbital of the metal to anti-bonding molecular orbitals of CO (and its analogs). This electron-transfer strengthens the metal–C bond and weakens the C–O bond. The strengthening of the M–CO bond is reflected in increases of the vibrational frequencies for the M–C bond (often outside of the range for the usual IR spectrophotometers). Furthermore, the M–CO bond length is shortened. The weakening of the C–O bond is indicated by a decrease in the wavenumber of the νCO band(s) from that for free CO (2143 cm−1), for example to 2060 cm−1 in Ni(CO)4 and 1981 cm−1 in Cr(CO)6, and 1790 cm−1 in the anion [Fe(CO)4]2−. For this reason, IR spectroscopy is an important diagnostic technique in metal–carbonyl chemistry. The article infrared spectroscopy of metal carbonyls discusses this in detail.

Many ligands other than CO are strong "backbonders". Nitric oxide is an even stronger π-acceptor than CO and νNO is a diagnostic tool in metal–nitrosyl chemistry. Isocyanides, RNC, are another class of ligands that are capable of π-backbonding. In contrast with CO, the σ-donor lone pair on the C atom of isocyanides is antibonding in nature and upon complexation the CN bond is strengthened and the νCN increased. At the same time, π-backbonding lowers the νCN. Depending on the balance of σ-bonding versus π-backbonding, the νCN can either be raised (for example, upon complexation with weak π-donor metals, such as Pt(II)) or lowered (for example, upon complexation with strong π-donor metals, such as Ni(0)). For the isocyanides, an additional parameter is the MC=N–C angle, which deviates from 180° in highly electron-rich systems. Other ligands have weak π-backbonding abilities, which creates a labilization effect of CO, which is described by the cis effect.

Metal–alkene and metal–alkyne complexes
As in metal–carbonyls, electrons are partially transferred from a d-orbital of the metal to antibonding molecular orbitals of the alkenes and alkynes. This electron transfer strengthens the metal–ligand bond and weakens the C–C bonds within the ligand. In the case of metal-alkenes and alkynes, the strengthening of the M–C2R4 and M–C2R2 bond is reflected in bending of the C–C–R angles which assume greater sp3 and sp2 character, respectively. Thus strong π backbonding causes a metal-alkene complex to assume the character of a metallacyclopropane. Alkenes and alkynes with electronegative substituents exhibit greater π backbonding. Some strong π backbonding ligands are tetrafluoroethylene, tetracyanoethylene, and hexafluoro-2-butyne.

Metal-phosphine complexes
Phosphines accept electron density from metal p or d orbitals into combinations of P–C σ* antibonding orbitals that have π symmetry. When phosphines bond to electron-rich metal atoms, backbonding would be expected to lengthen P–C bonds as P–C σ* orbitals become populated by electrons. The expected lengthening of the P–C distance is often hidden by an opposing effect: as the phosphorus lone pair is donated to the metal, P(lone pair)–R(bonding pair) repulsions decrease, which acts to shorten the P–C bond. The two effects have been deconvoluted by comparing the structures of pairs of metal-phosphine complexes that differ only by one electron. Oxidation of R3P–M complexes results in longer M–P bonds and shorter P–C bonds, consistent with π-backbonding. In early work, phosphine ligands were thought to utilize 3d orbitals to form M–P pi-bonding, but it is now accepted that d-orbitals on phosphorus are not involved in bonding as they are too high in energy.

IUPAC definition of Back Donation
The full IUPAC definition of back donation is as follows: A description of the bonding of π-conjugated ligands to a transition metal which involves a synergic process with donation of electrons from the filled π-orbital or lone electron pair orbital of the ligand into an empty orbital of the metal (donor–acceptor bond), together with release (back donation) of electrons from an nd orbital of the metal (which is of π-symmetry with respect to the metal–ligand axis) into the empty π*-antibonding orbital of the ligand.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Pi backbonding


text:
Talk:Zoot suit

Chicano
Chicano, I am pretty sure, is a 1960's neologism, so it is an anachronism in this article. Pachuco might be substituted, but I don't think that is quite right either. I'll try to do some research for a more appropriate term. gK [[User talk:GK|¿?]] 09:02, 4 Dec 2004 (UTC)

Chicano was around since at least the WWI era. It's use was strictly a perjorative, usually given by Mexican born parents to criticize their americanized progeny (It still has a negative connotation amongst recent immigrants from Mexico). In the Chicano Movement of the 1960s, however, it's meaning was appropriated to mean a politically an/or culturally conscious Mexican American. It has been somewhat been tied to the gang culture since the 1970s and therefore carries a negative meaning outside of artistic and collegiate circles. Pozole 05:29, 22 November 2005 (UTC)

2nd Picture of the Guys in "Zoot Suits"
As remarked on below in the section entitled "wedding image," the men in the picture are NOT wearing authentic Zoot Suits. They are wearing Zoot Tuxes. I visited the main location of the company El Pachuco and they told me authentic Zoot Suits do not have vests. The point of the style was to show off the high waist and suspenders. A Zoot Tux with a vest is basically just a long coat because it conceals the high waist and suspenders. So the caption of the picture needs to be changed but I don't know how to change it. Thanks. HuronKing Sunday January 25th. —Preceding unsigned comment added by 69.106.202.25 (talk) 22:34, 25 January 2009 (UTC)

Yeah but the caption is hilarious. --71.173.214.181 (talk) 18:42, 20 October 2010 (UTC)

Origin of zoot
"zoot" is a commonly used term for a marijuana cigarette. I think this deserves a mention, or at least some searching for references to a possible link. Apologies I can't be that person! — Preceding unsigned comment added by 109.145.32.141 (talk) 17:02, 5 March 2013 (UTC)

Could somebody verifiy the authenticity of this line:
 * The word "zoot" probably comes from the French word zut (meaning "damn!")

It seems a bit shady to me, and I don't have the time at the moment to check it out myself. – ClockworkSoul 14:46, 14 December 2005 (UTC)

I'm not sure on the authenticity of the line, but the translation of zut is wrong. Zut means "darn!" unless I've learned nothing in my 3 years of French.--Penarestel 22:39, 14 December 2005 (UTC)

 * So what's the difference between "damn" and "darn"? PeteVerdon 15:30, 3 January 2006 (UTC)

 * Depends on where you are in the world. One can be offensive and the other not.--Penarestel 05:28, 17 February 2006 (UTC)

When I was in high school in the 70s, classmates used to speak of someone being "zooted," meaning drunk or high. That made me think of the suit as something you'd wear in the context where people would be zooted, or where the wearer intends to be. I've also seen the use of "high-zoot" to mean powerful or expensive, which makes me doubt that the word came from a mispronunciation of "suit." 163.151.2.10 (talk) 14:08, 14 July 2009 (UTC)

Zoot Suit Riots
I am uncomfortable with the biased approach to discussing the race riots here. A more unbiased approach is suggested.

You need to sign your comment. {Registered editor snobbery!} You also need to specify exactly what it is you think is biased. Tmangray 00:26, 15 April 2006 (UTC)

removal of pachuca
I removed Pachuca as see also. This is a city, not equal to a Pachuco in the USA sense of the word. Additionaly, females associated with pachucos rarely(if ever)wore the same clothes as their male counterparts...I am also removing See also for the tom and jerry cartoon as this is not an existing article. If it were, it would still be better as a "reference in popular culture" --Ccosta 00:54, 1 June 2006 (UTC)

Broken link
The external link at the bottom doesn't seem to work... Is there a new address for it? -Russia Moore 01:33, 30 August 2006 (UTC)

Rowing Zoot Suit
So how in the world did Zoot Suit come to mean the things we wear while rowing? The tight rowing suits look nothing like "real" Zoot Suits. Strange indeed. Perhaps the ironic Aussie sense of humour at work?--ABVS 05:26, 31 October 2006 (UTC)

Article Improvement?
Great umbrage is taken to the recent editing of this page which eliminated "African Americans" and "Filipino Americans" from the listed ethnicities who "popularized" this style of clothing in the late 1930s and 1940s and also to the removal of the reference "Harlem Jazz culture" under the "History" heading.

The current interest of the WikiProject Mexican American should not override the fact that the zoot suit is indisputably an "invention" of the urban, swing jazz-related, African American "hep cat" culture of the day; and while the Pachuco connection (before, during and after the Los Angeles turmoil of 1943) clearly warrants extended discussion, it is tangential to the primary subject; and a separate page should be created to address this need.

Meanwhile, this page would be greatly enhanced by reverting to the previous wording and including a properly captioned photograph of the renowned Black entertainer Cab Calloway--on stage in the 1940s and wearing his trademark zoot suit--a vision that should be more evocative and symbolic than any other to aficionados of the style, be they Afro-, Filipino-, Anglo- or Latino-American. (Additionally, a bona fide pop culture icon like Calloway certainly deserves top billing over the cartoon "hepster" imitations--Li'l Abner and Tom and Jerry--who are now featured on the page.)

The Black-oriented films "Stormy Weather" (1943) and "Malcolm X" (1992) should also be listed with the others on this page for their celebration of the zoot suit; and Wikipedia's "Cab Calloway" page (itself greatly in need of enhancements) along with "The Zoot Suit and Style Warfare" page at  (among other references) should be listed on this page and any tangential ones that may be created. (151.200.123.149 06:23, 14 January 2007 (UTC))
 * These are all good points. I especially agree with your statement about restructuring the article to be more about the Zoot Suit rather than cartoons.  Per your comments I have looked for public domain images of Cab Calloway in the trademark clothing, but have only found the copy-righted variety on the web.  Did you have any picture resources in mind?  I have been meaning to improve this article for some time just haven't found the time.  I encourage you to be bold and edit the article yourself (i.e., it may be a long time before anyone else gets around to it).  Thank you for the comments!--Will.i.am 21:50, 14 January 2007 (UTC)
 * I concur with the umbrage re: removing the actual origin of the zoot suit. The zoot suit first appears in the 1930s in New York as "drapes" among African American youths.  The name "zoot suit" appears to be original to Los Angeles and pachuco slang, and was subsequently used even in NYC. Tmangray 06:56, 18 January 2007 (UTC)

The Introduction and Table of Contents for Mauricio Mazón's book, "The Zoot-Suit Riots: The Psychology of Symbolic Annihilation" is available at . Published in 1984 by University of Texas Press, this information may help clarify needed additions that pertain to Latino and El Paso ("El Chuco"), Texas aspects of this article.

In addition, "Pachuco, Tirilon, and Chicano" by Lurline H. Coltharp is available through JSTOR or the original journal "American Speech," Vol. 50, No 1/2 1975, pp. 25-29 for researched linguistic information on the subject terms.

--chacal la chaise 06:14, 26 May 2007 (UTC)

Low Waist / High Waist / Pleats
I noticed while reverting vandalism that someone had changed "low waisted" to "high waisted". A small correction or subtle vandalism? I don't know if zoot suits SHOULD be high or low waisted, so I'll leave it in someone else's hands.

When Zoot Suits were first around, they were "high waisted". So technically, the suits should be "high waisted". My reference is my grandfather who was around for the peak of Zoot Suit popularity and was an avid wearer in his heyday. -ExodusFire

High Waisted is right.

I have always heard "reet pleats" paired with Zoot Suit in "hip" talk, ie: "A Zoot Suit With Reet Pleats". Shouldn't that get a mention.

Capitalization
I think we should come to a consensus over the capitalization of 'zoot suit' across Wikipedia. The article itself uses two forms of capitalization, 'zoot suit' and 'Zoot Suit', as does the Pachuco article. Personally I think it should be all lower-case but that's just my humble opinion. -Andreas Toth (talk) 23:45, 26 February 2008 (UTC)

Wedding Image
The men wearing the suits for the wedding are definitelt not Zoot suits. —Preceding unsigned comment added by 80.94.35.227 (talk) 11:21, 4 September 2008 (UTC)

Yes you are right, they are wearing Zoot Tuxes, not actual Zoot Suits. HuronKing, Tuesday January 20th 2009 —Preceding unsigned comment added by 69.106.202.25 (talk) 04:36, 21 January 2009 (UTC)

Creation
(comments moved here from article space)

I am not certain who gave the name “Zoot Suit” to this garment, but it was my father, Nathan “Toddy” Elkus who actually designed the garment later so named. It was back in the spring of 1939 when my Dad took a regular suit, marked it with a host of chalk marks and sent off to Blankson Clothes of New York have a sample garment made. I was there when the sample suit came back from New York and my Dad opened the package. He was furious because Blankson had made the suit with regular pockets instead of slash pockets and had a regular button front instead of a fly front. Long distance calls in those days were a costly rarity, but my Dad called Mr. Irving Blank and insisted upon having both slash pockets and a fly front.

Mr. Blank refused to make the suit with those extra styling details remarking, “A dozen eggs won’t guarantee a sponge cake will rise!” My Dad insisted and finally Mr. Blank told him he’ll manufacture the suits, but he’ll have to pay for them up-front with the order and the sale would be final, absolutely no returns, period. My Dad airmailed a certified check that day for 100 suits, a major cutting in those days….and the rest is history.

When the suits arrived 6 weeks later, he named the suits the “Thunderbird” and toyed with the idea of a window display showing the then popular “Ace” suit in a coffin, with the new “Thunderbolt” (later to be named the zoot suit) on a mannequin standing on the coffin. But the manager of the store reminded him that he had hundreds of older suits in stock and couldn’t afford to declare all of them dead. So the Thunderbolt went on display as a new model in all its glory in my Dad’s store, Todd’s Clothes in Detroit. It was an immediate success. The details of the original suit: 32” length coat on a 40 regualr, with a 20” shoulder, single breasted, fly front, slash pockets, wqith a one piece back. The trousers were a high rise, pg legs with a 30 inch knee and 15 inch bottom. With all due respect to Mr. Fox, who may have named it the Zoot Suit, it was my father, Nathan Elkus, who created it. Philip Elkus —Preceding unsigned comment added by 76.108.142.128 (talk • contribs)

 * I've moved the above comments (copy of a 1996 letter to the editor of the NY Times) here from the article and reworded the "Creation" paragraph to mention all three claimants, with citations for each. Since even the NY Times seems ambivalent about naming a creator, until some tiebreaker information from a reliable source is found, readers will have to read the citations and decide for themselves.  --CliffC (talk) 03:37, 26 December 2008 (UTC)

 * I propose the merger of the Creation and History sections. In doing so, the various stories can be laid out regarding the origin of the style and the name. Tmangray (talk) 05:34, 1 January 2009 (UTC)

 * Sounds good to me. Happy new year!  --CliffC (talk) 17:44, 1 January 2009 (UTC)

Capitalization revisited
Seeing as how nobody responded to this inquiry, I plan to change all instances of the terms "Zoot suit", "Zoot Suit", etc., on Wikipedia to lower case form, "zoot suit". Any objections? Lord Sesshomaru (talk • edits) 16:53, 31 December 2008 (UTC)

 * FWIW, the New York Times lowercases the term, examples here. --CliffC (talk) 02:26, 1 January 2009 (UTC)

You are wrong. In the 1943 Laurel and Hardy movie "Jitterbugs" they drive round in a van with "The original Zoot Suit Band" on the side. So not only is your assumption its in lower case wrong, you also lack in the wiki or page any reference to the concept of a "Zoot Suit Band" which were extant in the 1940's and 50's and was a distinct style of act.

https://www.imdb.com/title/tt0036055/

2.59.114.197 (talk) 11:38, 11 July 2021 (UTC)

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Pop Culture
I think we need a "Pop Culture" section for various famous appearances of Zoot Suits.

For instance there is a memorable classic "Tom & Jerry" short featuring both characters courting in Zoot Suits.

Also, there was a memorable sequence in Jim Carrey's "The Mask" done in a yellow Zoot Suit (https://www.youtube.com/watch?v=iqjq2s_bHPA) — Preceding unsigned comment added by 108.202.33.17 (talk) 20:49, 15 August 2018 (UTC)

Historically, this article stops with Malcolm X
A whole article about Zoot Suits and no mention about pimps at all?

Drsruli (talk) 07:01, 2 August 2021 (UTC)

A Commons file used on this page or its Wikidata item has been nominated for speedy deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for speedy deletion: You can see the reason for deletion at the file description page linked above. —Community Tech bot (talk) 23:53, 31 October 2022 (UTC)
 * Louis Jordan Movie poster "Caldonia".jpg

two things
one use of pegged in the intro is jargon; spell it out two most of the photos are not that good; comnpar to this one https://www.mylesanthony.co.uk/zoot-suit-style-wedding/ honestly, all the effort into words, and all the pointless debate here in the talk section and no one can find a really decent photo ?????? — Preceding unsigned comment added by 2601:197:D00:3CA0:8C25:9FB1:515D:29CA (talk) 16:27, 3 June 2023 (UTC)

title: Talk:Zoot suit


text:
Wad

WAD, Wad, or wad may refer to:

People

 * Joan the Wad, a mythological character in Cornish folklore
 * Nishigandha Wad (born 1969), Indian film actress
 * William Addison Dwiggins (1880–1956), American type and graphic designer known by his initials

Science and technology

 * Doom WAD, the default format of package files for the id Tech 1 game engine. Stands for "Where's All the Data?"
 * Wad (mineral), any black manganese oxide or hydroxide mineral rich rock of various ore deposits
 * WAD, the IATA airport code for Andriamena Airport, Andriamena, Madagascar
 * Wadding, disc of material used in guns
 * Wii WAD, a file archive which can be used on a Wii gaming console via homebrew software
 * Web Accessibility Directive, EU law that ensures that all public sector organizations are accessible for persons with disabilities.
 * "whiplash associated disorder" is a colloquial name in medicine

Other uses

 * wad, the Dutch term for a mud flat on the Wadden Sea
 * Wretched and Divine: The Story of the Wild Ones, a 2013 album by American rock band Black Veil Brides

title: Wad


text: User talk:68.79.195.103

title: User talk:68.79.195.103


text:
Hyaluronic acid

Hyaluronic acid (abbreviated HA; conjugate base hyaluronate), also called hyaluronan, is an anionic, nonsulfated glycosaminoglycan distributed widely throughout connective, epithelial, and neural tissues. It is unique among glycosaminoglycans as it is non-sulfated, forms in the plasma membrane instead of the Golgi apparatus, and can be very large: human synovial HA averages about 7 million Da per molecule, or about 20,000 disaccharide monomers, while other sources mention 3–4 million Da.

The average 70 kg (150 lb) person has roughly 15 grams of hyaluronan in the body, one third of which is turned over (i.e., degraded and synthesized) per day.

As one of the chief components of the extracellular matrix, it contributes significantly to cell proliferation and migration, and is involved in the progression of many malignant tumors. Hyaluronic acid is also a component of the group A streptococcal extracellular capsule, and is believed to play a role in virulence.

Physiological function
Until the late 1970s, hyaluronic acid was described as a "goo" molecule, a ubiquitous carbohydrate polymer that is part of the extracellular matrix. For example, hyaluronic acid is a major component of the synovial fluid and was found to increase the viscosity of the fluid. Along with lubricin, it is one of the fluid's main lubricating components.

Hyaluronic acid is an important component of articular cartilage, where it is present as a coat around each cell (chondrocyte). When aggrecan monomers bind to hyaluronan in the presence of HAPLN1 (hyaluronic acid and proteoglycan link protein 1), large, highly negatively charged aggregates form. These aggregates imbibe water and are responsible for the resilience of cartilage (its resistance to compression). The molecular weight (size) of hyaluronan in cartilage decreases with age, but the amount increases.

A lubricating role of hyaluronan in muscular connective tissues to enhance the sliding between adjacent tissue layers has been suggested. A particular type of fibroblasts, embedded in dense fascial tissues, has been proposed as being cells specialized for the biosynthesis of the hyaluronan-rich matrix. Their related activity could be involved in regulating the sliding ability between adjacent muscular connective tissues.

Hyaluronic acid is also a major component of skin, where it is involved in repairing tissue. When skin is exposed to excessive UVB rays, it becomes inflamed (sunburn), and the cells in the dermis stop producing as much hyaluronan and increase the rate of its degradation. Hyaluronan degradation products then accumulate in the skin after UV exposure.

While it is abundant in extracellular matrices, hyaluronan also contributes to tissue hydrodynamics, movement, and proliferation of cells and participates in a number of cell surface receptor interactions, notably those including its primary receptors, CD44 and RHAMM. Upregulation of CD44 itself is widely accepted as a marker of cell activation in lymphocytes. Hyaluronan's contribution to tumor growth may be due to its interaction with CD44. Receptor CD44 participates in cell adhesion interactions required by tumor cells.

Although hyaluronan binds to receptor CD44, there is evidence hyaluronan degradation products transduce their inflammatory signal through toll-like receptor 2 (TLR2), TLR4, or both TLR2 and TLR4 in macrophages and dendritic cells. TLR and hyaluronan play a role in innate immunity.

There are limitations including the in vivo loss of this compound limiting the duration of effect.

Wound repair
As a major component of the extracellular matrix, hyaluronic acid has a key role in tissue regeneration, inflammation response, and angiogenesis, which are phases of wound repair. As of 2023, however, reviews of its effect on healing for chronic wounds including burns, diabetic foot ulcers or surgical skin repairs show either insufficient evidence or only limited positive clinical research evidence. There is also some limited evidence to suggest that hyaluronic acid may be beneficial for ulcer healing and may help to a small degree with pain control. Hyaluronic acid combines with water and swells to form a gel, making it useful in skin treatments as a dermal filler for facial wrinkles; its effect lasts for about 6 to 12 months, and treatment has regulatory approval from the US Food and Drug Administration.

Granulation
Granulation tissue is the perfused, fibrous connective tissue that replaces a fibrin clot in healing wounds. It typically grows from the base of a wound and is able to fill wounds of almost any size it heals. HA is abundant in granulation tissue matrix. A variety of cell functions that are essential for tissue repair may attribute to this HA-rich network. These functions include facilitation of cell migration into the provisional wound matrix, cell proliferation, and organization of the granulation tissue matrix. Initiation of inflammation is crucial for the formation of granulation tissue; therefore, the pro-inflammatory role of HA as discussed above also contributes to this stage of wound healing.

Cell migration
Cell migration is essential for the formation of granulation tissue. The early stage of granulation tissue is dominated by a HA-rich extracellular matrix, which is regarded as a conducive environment for the migration of cells into this temporary wound matrix. HA provides an open hydrated matrix that facilitates cell migration, whereas, in the latter scenario, directed migration and control of related cell mechanisms are mediated via the specific cell interaction between HA and cell surface HA receptors. It forms links with several protein kinases associated with cell locomotion, for example, extracellular signal-regulated kinase, focal adhesion kinase, and other non-receptor tyrosine kinases. During fetal development, the migration path through which neural crest cells migrate is rich in HA. HA is closely associated with the cell migration process in granulation tissue matrix, and studies show that cell movement can be inhibited, at least partially, by HA degradation or blocking HA receptor occupancy.

By providing the dynamic force to the cell, HA synthesis has also been shown to associate with cell migration. Basically, HA is synthesized at the plasma membrane and released directly into the extracellular environment. This may contribute to the hydrated microenvironment at sites of synthesis, and is essential for cell migration by facilitating cell detachment.

Skin healing
HA plays an important role in the normal epidermis. HA also has crucial functions in the reepithelization process due to several of its properties. These include being an integral part of the extracellular matrix of basal keratinocytes, which are major constituents of the epidermis; its free-radical scavenging function, and its role in keratinocyte proliferation and migration.

In normal skin, HA is found in relatively high concentrations in the basal layer of the epidermis where proliferating keratinocytes are found. CD44 is collocated with HA in the basal layer of epidermis where additionally it has been shown to be preferentially expressed on plasma membrane facing the HA-rich matrix pouches. Maintaining the extracellular space and providing an open, as well as hydrated, structure for the passage of nutrients are the main functions of HA in epidermis. A report found HA content increases in the presence of retinoic acid (vitamin A). The proposed effects of retinoic acid against skin photo-damage and photoaging may be correlated, at least in part, with an increase of skin HA content, giving rise to increased tissue hydration. It has been suggested that the free-radical scavenging property of HA contributes to protection against solar radiation, supporting the role of CD44 acting as a HA receptor in the epidermis.

Epidermal HA also functions as a manipulator in the process of keratinocyte proliferation, which is essential in normal epidermal function, as well as during reepithelization in tissue repair. In the wound healing process, HA is expressed in the wound margin, in the connective tissue matrix, and collocating with CD44 expression in migrating keratinocytes.

Medical uses
Hyaluronic acid has been FDA-approved to treat osteoarthritis of the knee via intra-articular injection. A 2012 review showed that the quality of studies supporting this use was mostly poor, with a general absence of significant benefits, and that intra-articular injection of HA could possibly cause adverse effects. A 2020 meta-analysis found that intra-articular injection of high molecular weight HA improved both pain and function in people with knee osteoarthritis.

Hyaluronic acid has been used to treat dry eye. Hyaluronic acid is a common ingredient in skin care products. Hyaluronic acid is used as a dermal filler in cosmetic surgery. It is typically injected using either a classic sharp hypodermic needle or a micro-cannula. Some studies have suggested that the use of micro-cannulas can significantly reduce vessel embolisms during injections. Currently, hyaluronic acid is used as a soft tissue filler due to its bio-compatibility and possible reversibility using hyaluronidase. Complications include the severing of nerves and microvessels, pain, and bruising. Some side effects can also appear by way of erythema, itching, and vascular occlusion; vascular occlusion is the most worrisome side effect due to the possibility of skin necrosis, or even blindness in a patient. In some cases, hyaluronic acid fillers can result in a granulomatous foreign body reaction.

Hyaluronic acid is used to displace tissues away from tissues which are going to be subjected to radiation, for instance in one treatment option for some prostate cancers.

Structure
Hyaluronic acid is a polymer of disaccharides, which are composed of D -glucuronic acid and N-acetyl- D -glucosamine, linked via alternating β-(1→4) and β-(1→3) glycosidic bonds. Hyaluronic acid can be 25,000 disaccharide repeats in length. Polymers of hyaluronic acid can range in size from 5,000 to 20,000,000 Da in vivo. The average molecular weight in human synovial fluid is 3–4 million Da, and hyaluronic acid purified from human umbilical cord is 3,140,000 Da; other sources mention average molecular weight of 7 million Da for synovial fluid. Hyaluronic acid also contains silicon, ranging 350–1,900μg/g depending on location in the organism.

Hyaluronic acid is energetically stable, in part because of the stereochemistry of its component disaccharides. Bulky groups on each sugar molecule are in sterically favored positions, whereas the smaller hydrogens assume the less-favorable axial positions.

Hyaluronic acid in aqueous solutions self-associates to form transient clusters in solution. While it is considered a polyelectrolyte polymer chain, hyaluronic acid does not exhibit the polyelectrolyte peak, suggesting the absence of a characteristic length scale between the hyaluronic acid molecules and the emergence of a fractal clustering, which is due to the strong solvation of these molecules.

Biological synthesis
Hyaluronic acid is synthesized by a class of integral membrane proteins called hyaluronan synthases, of which vertebrates have three types: HAS1, HAS2, and HAS3. These enzymes lengthen hyaluronan by repeatedly adding D -glucuronic acid and N-acetyl- D -glucosamine to the nascent polysaccharide as it is extruded via ABC-transporter through the cell membrane into the extracellular space. The term fasciacyte was coined to describe fibroblast-like cells that synthesize HA.

Hyaluronic acid synthesis has been shown to be inhibited by 4-methylumbelliferone (hymecromone), a 7-hydroxy-4-methylcoumarin derivative. This selective inhibition (without inhibiting other glycosaminoglycans) may prove useful in preventing metastasis of malignant tumor cells. There is feedback inhibition of hyaluronan synthesis by low-molecular-weight hyaluronan (<500 kDa) at high concentrations, but stimulation by high-molecular-weight hyaluronan (>500 kDa), when tested in cultured human synovial fibroblasts.

Bacillus subtilis recently has been genetically modified to culture a proprietary formula to yield hyaluronans, in a patented process producing human-grade product.

Fasciacyte
A fasciacyte is a type of biological cell that produces hyaluronan-rich extracellular matrix and modulates the gliding of muscle fasciae.

Fasciacytes are fibroblast-like cells found in fasciae. They are round-shaped with rounder nuclei and have less elongated cellular processes when compared with fibroblasts. Fasciacytes are clustered along the upper and lower surfaces of a fascial layer.

Fasciacytes produce hyaluronan, which regulates fascial gliding.

Biosynthetic mechanism
Hyaluronic acid (HA) is a linear glycosaminoglycan (GAG), an anionic, gel-like, polymer, found in the extracellular matrix of epithelial and connective tissues of vertebrates. It is part of a family of structurally complex, linear, anionic polysaccharides. The carboxylate groups present in the molecule make it negatively charged, therefore allowing for successful binding to water, and making it valuable to cosmetic and pharmaceutical products.

HA consists of repeating β4-glucuronic acid (GlcUA)-β3-N-acetylglucosamine (GlcNAc) disaccharides, and is synthesized by hyaluronan synthases (HAS), a class of integral membrane proteins that produce the well-defined, uniform chain lengths characteristic to HA. There are three existing types of HASs in vertebrates: HAS1, HAS2, HAS3; each of these contribute to elongation of the HA polymer. For an HA capsule to be created, this enzyme must be present because it polymerizes UDP-sugar precursors into HA. HA precursors are synthesized by first phosphorylating glucose by hexokinase, yielding glucose-6-phosphate, which is the main HA precursor. Then, two routes are taken to synthesize UDP-n-acetylglucosamine and UDP-glucuronic acid which both react to form HA. Glucose-6-phosphate gets converted to either fructose-6-phosphate with hasE (phosphoglucoisomerase), or glucose-1-phosphate using pgm (α -phosphoglucomutase), where those both undergo different sets of reactions.

UDP-glucuronic acid and UDP-n-acetylglucosamine get bound together to form HA via hasA (HA synthase).

Synthesis of UDP-glucuronic acid
UDP-glucuronic acid is formed from hasC (UDP-glucose pyrophosphorylase) converting glucose-1-P into UDP-glucose, which then reacts with hasB (UDP-glucose dehydrogenase) to form UDP-glucuronic acid.

Synthesis of N-acetyl glucosamine
The path forward from fructose-6-P utilizes glmS (amidotransferase) to form glucosamine-6-P. Then, glmM (Mutase) reacts with this product to form glucosamine-1-P. hasD (acetyltransferase) converts this into n-acetylglucosamine-1-P, and finally, hasD (pyrophosphorylase) converts this product into UDP-n-acetylglucosamine.

Final step: Two disaccharides form hyaluronic acid
UDP-glucuronic acid and UDP-n-acetylglucosamine get bound together to form HA via hasA (HA synthase), completing the synthesis.

Degradation
Hyaluronic acid can be degraded by a family of enzymes called hyaluronidases. In humans, there are at least seven types of hyaluronidase-like enzymes, several of which are tumor suppressors. The degradation products of hyaluronan, the oligosaccharides and very low-molecular-weight hyaluronan, exhibit pro-angiogenic properties. In addition, recent studies showed hyaluronan fragments, not the native high-molecular weight molecule, can induce inflammatory responses in macrophages and dendritic cells in tissue injury and in skin transplant.

Hyaluronan can also be degraded via non-enzymatic reactions. These include acidic and alkaline hydrolysis, ultrasonic disintegration, thermal decomposition, and degradation by oxidants.

Etymology
Hyaluronic acid is derived from hyalos (Greek for vitreous, meaning ‘glass-like’) and uronic acid because it was first isolated from the vitreous humour and possesses a high uronic acid content. The term hyaluronate refers to the conjugate base of hyaluronic acid. Since the molecule typically exists in vivo in its polyanionic form, it is most commonly referred to as hyaluronan.

History
Hyaluronic acid was first obtained by Karl Meyer and John Palmer in 1934 from the vitreous body in a cow's eye. The first hyaluronan biomedical product, Healon, was developed in the 1970s and 1980s by Pharmacia, and approved for use in eye surgery (i.e., corneal transplantation, cataract surgery, glaucoma surgery, and surgery to repair retinal detachment). Other biomedical companies also produce brands of hyaluronan for ophthalmic surgery.

Native hyaluronic acid has a relatively short half-life (shown in rabbits) so various manufacturing techniques have been deployed to extend the length of the chain and stabilise the molecule for its use in medical applications. The introduction of protein-based cross-links, the introduction of free-radical scavenging molecules such as sorbitol, and minimal stabilisation of the HA chains through chemical agents such as NASHA (non-animal stabilised hyaluronic acid) are all techniques that have been used to preserve its shelf life.

In the late 1970s, intraocular lens implantation was often followed by severe corneal edema, due to endothelial cell damage during the surgery. It was evident that a viscous, clear, physiologic lubricant to prevent such scraping of the endothelial cells was needed.

The name "hyaluronan" is also used for a salt.

Other animals
Hyaluronan is used in treatment of articular disorders in horses, in particular those in competition or heavy work. It is indicated for carpal and fetlock joint dysfunctions, but not when joint sepsis or fracture are suspected. It is especially used for synovitis associated with equine osteoarthritis. It can be injected directly into an affected joint, or intravenously for less localized disorders. It may cause mild heating of the joint if directly injected, but this does not affect the clinical outcome. Intra-articularly administered medicine is fully metabolized in less than a week.

According to Canadian regulation, hyaluronan in HY-50 preparation should not be administered to animals to be slaughtered for horse meat. In Europe, however, the same preparation is not considered to have any such effect, and edibility of the horse meat is not affected.

Research
Due to its accumulation in airway epithelial cells in various respiratory diseases, such as COVID-19, cystic fibrosis, influenza, and sepsis, hyaluronic acid is under study as a possible mediator of lung inflammatory mechanisms, as of 2022.

The high biocompatibility of hyaluronic acid and its common presence in the extracellular matrix of tissues indicate its possible use as a biomaterial scaffold in tissue engineering. In particular, research groups have found hyaluronan's properties for tissue engineering and regenerative medicine may be improved with cross-linking, producing a hydrogel. Crosslinking may allow a desired shape, as well as to deliver therapeutic molecules into a host. Hyaluronan can be crosslinked by attaching thiols (see thiomers) (trade names: Extracel, HyStem), hexadecylamides (trade name: Hymovis), and tyramines (trade name: Corgel). Hyaluronan can also be crosslinked directly with formaldehyde (trade name: Hylan-A) or with divinylsulfone (trade name: Hylan-B).

Due to its ability to regulate angiogenesis by stimulating endothelial cells to proliferate in vitro, hyaluronan can be used to create hydrogels to study vascular morphogenesis.

title: Hyaluronic acid


text:
Category:Glycosaminoglycans

Glycosaminoglycans (GAGs) are long unbranched polysaccharides consisting of a repeating disaccharide unit. The general disaccharide unit consists of an N-acetyl-hexosamine and a hexose or hexuronic acid, either or both of which may be sulfated. Members of the glycosaminoglycan family differ in the type of hexosamine, hexose or hexuronic acid they contain and the geometry of the glycosidic linkages.

title: Category:Glycosaminoglycans


text: User talk:66.112.3.65

title: User talk:66.112.3.65


text:
Talk:Langley, Washington

Langley by the Sea?
I lived in Langley and not once did I ever hear it referred to as "Langley by the Sea." It's ridiculous. So I deleted it. —Preceding unsigned comment added by Isoruku (talk • contribs) 03:22, 31 August 2009 (UTC)

 * But langley is by the sea. — Preceding unsigned comment added by 66.235.71.235 (talk) 14:31, 30 May 2016 (UTC)

I am a former member of the Langley Chamber of Commerce, and for some time the phrase "village by the sea" was used in marketing communications by the chamber and other organizations. The subtitle of the City Government's website is currently "The Village by the sea" DionJohnstone (talk) 00:20, 13 April 2017 (UTC)

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Discrepancy in total area
The "Geography" section states "the city has a total area of 1.08 square miles (2.80 sqkm), all of it land". The Infobox has 1.01 sq mi for the land area and includes some water area also. Could someone resolve this issue? Tagooty (talk) 16:10, 17 February 2024 (UTC)

 * A further discrepancy: the 1st para in the lead section mentions 0.8 sq mi. Tagooty (talk) 04:44, 18 February 2024 (UTC)

Hi b 46.188.186.72 (talk) 07:28, 25 April 2024 (UTC)

title: Talk:Langley, Washington


text:
Teenager (Jane Siberry album)

Teenager is a 1996 album by Jane Siberry.

It was her first release for Sheeba Records, the independent label she established for herself after the end of her contract with Reprise Records. The album is composed of songs that Siberry had written as a teenager, but had never subsequently released on record.

Critical reception
The Dallas Observer called the album "13 supple, unadorned songs," writing that "lovely, reflective tunes like 'Puppet City' and 'Viking Heart' offer thrillingly adult looks at, respectively, emotional paralysis and the enticements of a handsome, attentive stranger."

Track listing

 * 1) "Introduction" – 0:27
 * 2) "The Squirrel Crossed the Road" – 5:13
 * 3) "Let's Not Talk Now" – 4:05
 * 4) "Song to My Father" – 4:54
 * 5) "Broken Birds" – 5:09
 * 6) "Puppet City" – 4:28
 * 7) "Oh My Sister" – 3:56
 * 8) "The Long Pirouette" – 4:33
 * 9) "Bessie" – 3:37
 * 10) "We Should Be There by Morning" – 4:17
 * 11) "Viking Heart" – 6:24
 * 12) "When Spring Comes" – 3:25
 * 13) "Angel Voyeur" – 5:50
 * 14) "Trumpeter Swan" – 5:56

title: Teenager (Jane Siberry album)


text:
Sheeba Records

Sheeba Records is a Canadian independent record label, owned and operated by Jane Siberry.

Siberry established Sheeba to release her albums following the end of her contract with Reprise Records in 1996. The first album she released on the label was Teenager, a collection of songs she had written in her teenage years but had never released on record.

Since Siberry established Sheeba, she has released all of her albums on the label.

title: Sheeba Records