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Austrian German

Austrian German (Österreichisches Deutsch), Austrian Standard German (ASG), Standard Austrian German (Österreichisches Standarddeutsch), Austrian High German (Österreichisches Hochdeutsch), or simply just Austrian (Österreichisch), is the variety of Standard German written and spoken in Austria and South Tyrol. It has the highest sociolinguistic prestige locally, as it is the variation used in the media and for other formal situations. In less formal situations, Austrians use Bavarian and Alemannic dialects, which are traditionally spoken but rarely written in Austria. It has been standardized with the publishing of the Österreichisches Wörterbuch in 1951.

History
Austrian German has its beginning in the mid-18th century, when Empress Maria Theresa and her son Joseph II introduced compulsory schooling in 1774, and several reforms of administration in their multilingual Habsburg Empire. At the time, the written standard was Oberdeutsche Schreibsprache (Upper German written language), which was highly influenced by the Bavarian and Alemannic dialects of Austria. Another option was to create a new standard based on the Southern German dialects, as proposed by the linguist Johann Siegmund Popowitsch. Instead they decided for pragmatic reasons to adopt the already-standardized chancellery language of Saxony (Sächsische Kanzleisprache or Meißner Kanzleideutsch), which was based on the administrative language of the non-Austrian area of Meißen and Dresden. Austria High German (Hochdeutsch in Österreich, not to be confused with the Bavarian Austria German dialects) has the same geographic origin as the Swiss High German (Schweizer Hochdeutsch, not to be confused with the Alemannic Swiss German dialects).

The process of introducing the new written standard was led by Joseph von Sonnenfels.

Since 1951, the standardized form of Austrian German for official governmental use and in schools has been defined by the Österreichisches Wörterbuch ("Austrian Dictionary"), published originally at the behest of the Austrian Federal Ministry of Education, Arts and Culture (in the 1950s the "Unterrichtsministerium", under minister Felix Hurdes) with Verlag Jugend & Volk, then by the Österreichischer Bundesverlag.

Standard Austrian German
The official Austrian dictionary, Österreichisches Wörterbuch, prescribes spelling rules that define the official language.

Austrian delegates participated in the international working group that drafted the German spelling reform of 1996 and several conferences leading up to the reform were hosted in Vienna at the invitation of the Austrian federal government. Austria adopted it as a signatory, along with Germany, Switzerland, and Liechtenstein, of an international memorandum of understanding (Wiener Absichtserklärung) signed in Vienna in 1996.

The eszett or "sharp s" (ß) is used in Austria, as in Germany but not in Switzerland.

Distinctions in vocabulary persist, for example, in culinary terms, for which communication with Germans is frequently difficult, and administrative and legal language because of Austria's exclusion from the development of a German nation-state in the late 19th century and its manifold particular traditions. A comprehensive collection of Austrian-German legal, administrative and economic terms is offered in Markhardt, Heidemarie: Wörterbuch der österreichischen Rechts-, Wirtschafts- und Verwaltungsterminologie (Peter Lang, 2006).

Because of German's pluricentric nature, German dialects in Austria should not be confused with the variety of Standard Austrian German spoken by most Austrians, which is distinct from that of Germany or Switzerland. In the field of German dialectology, the notion of Standard Austrian German has been both debated and defended by German linguists since the 1970s. A One Standard German Axiom, effectively preventing the development of newer standards of German, has recently been offered as a characteristic of the field but has not been taken up.

Former spoken standard
Until 1918, the spoken standard in Austria was the Schönbrunner Deutsch, a sociolect spoken by the imperial Habsburg family and the nobility of Austria-Hungary. The sociolect, a variety of Standard German, is influenced by Viennese German and other Austro-Bavarian dialects spoken in eastern Austria but is slightly nasalized.

Special written forms
For many years, Austria had a special form of the language for official government documents that is known as Österreichische Kanzleisprache, or "Austrian chancellery language". It is a very traditional form of the language, probably derived from medieval deeds and documents, and has a very complex structure and vocabulary generally reserved for such documents. For most speakers (even native speakers), this form of the language is generally difficult to understand, as it contains many highly-specialised terms for diplomatic, internal, official, and military matters. There are no regional variations because the special written form has been used mainly by a government that has now for centuries been based in Vienna.

Österreichische Kanzleisprache is now used less and less because of various administrative reforms that reduced the number of traditional civil servants (Beamte). As a result, Standard Austrian German is replacing it in government and administrative texts.

European Union
When Austria became a member of the European Union, 23 food-related terms were listed in its accession agreement as having the same legal status as the equivalent terms used in Germany, for example, the words for "potato", "tomato", and "Brussels sprouts". (Examples in "Vocabulary") Austrian German is the only variety of a pluricentric language recognized under international law or EU primary law.

Verbs
In Austria, as in the German-speaking parts of Switzerland and in southern Germany, verbs that express a state tend to use sein as the auxiliary verb in the perfect, as well as verbs of movement. Verbs which fall into this category include sitzen (to sit), liegen (to lie) and, in parts of Styria and Carinthia, schlafen (to sleep). Therefore, the perfect of these verbs would be ich bin gesessen, ich bin gelegen and ich bin geschlafen, respectively.

In Germany, the words stehen (to stand) and gestehen (to confess) are identical in the present perfect: habe gestanden. The Austrian variant avoids that potential ambiguity (bin gestanden from stehen, "to stand"; and habe gestanden from gestehen, "to confess": "der Verbrecher ist vor dem Richter gestanden und hat gestanden").

In addition, the preterite (simple past) is very rarely used in Austria, especially in the spoken language, with the exception of some modal verbs (ich sollte, ich wollte).

Vocabulary
There are many official terms that differ in Austrian German from their usage in most parts of Germany. Words used in Austria are Jänner (January) rather than Januar, Feber (seldom, February) along with Februar, heuer (this year) along with dieses Jahr, Stiege (stairs) along with Treppen, Rauchfang (chimney) instead of Schornstein, many administrative, legal and political terms, and many food terms, including the following:

There are, however, some false friends between the two regional varieties:
 * Kasten (wardrobe) along with or instead of Schrank (and, similarly, Eiskasten along with Kühlschrank, fridge), as opposed to Kiste (box) instead of Kasten. Kiste in Germany means both "box" and "chest".
 * Sessel (chair) instead of Stuhl. Sessel means "" in Germany and Stuhl means "stool (faeces)" in both varieties.

Classification

 * Dialects of the Austro-Bavarian group, which also comprises dialects from Bavaria
 * Central Austro-Bavarian (along the main rivers Isar and Danube, spoken in the northern parts of the State of Salzburg, Upper Austria, Lower Austria, and northern Burgenland)
 * Viennese German
 * Southern Austro-Bavarian (in Tyrol, South Tyrol, Carinthia, Styria, and the southern parts of Salzburg and Burgenland)
 * Vorarlbergerisch, spoken in Vorarlberg, is a High Alemannic dialect.

Regional accents
In addition to the standard variety, in everyday life most Austrians speak one of a number of Upper German dialects.

While strong forms of the various dialects are not fully mutually intelligible to northern Germans, communication is much easier in Bavaria, especially rural areas, where the Bavarian dialect still predominates as the mother tongue. The Central Austro-Bavarian dialects are more intelligible to speakers of Standard German than the Southern Austro-Bavarian dialects of Tyrol.

Viennese, the Austro-Bavarian dialect of Vienna, is seen for many in Germany as quintessentially Austrian. The people of Graz, the capital of Styria, speak yet another dialect which is not very Styrian and more easily understood by people from other parts of Austria than other Styrian dialects, for example from western Styria.

Simple words in the various dialects are very similar, but pronunciation is distinct for each and, after listening to a few spoken words, it may be possible for an Austrian to realise which dialect is being spoken. However, in regard to the dialects of the deeper valleys of the Tyrol, other Tyroleans are often unable to understand them. Speakers from the different provinces of Austria can easily be distinguished from each other by their particular accents (probably more so than Bavarians), those of Carinthia, Styria, Vienna, Upper Austria, and the Tyrol being very characteristic. Speakers from those regions, even those speaking Standard German, can usually be easily identified by their accent, even by an untrained listener.

Several of the dialects have been influenced by contact with non-Germanic linguistic groups, such as the dialect of Carinthia, where, in the past, many speakers were bilingual (and, in the southeastern portions of the state, many still are even today) with Slovene, and the dialect of Vienna, which has been influenced by immigration during the Austro-Hungarian period, particularly from what is today the Czech Republic. The German dialects of South Tyrol have been influenced by local Romance languages, particularly noticeable with the many loanwords from Italian and Ladin.

The geographic borderlines between the different accents (isoglosses) coincide strongly with the borders of the states and also with the border with Bavaria, with Bavarians having a markedly different rhythm of speech in spite of the linguistic similarities.

title: Austrian German


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Talk:Acronym/Archive 3

New version
Nohat, please check out Acronym/temp2. I have made attempts to remove what I believe is the perceived POV, while keeping a clear distinction between acronyms and initialisms. Anárion Talk 08:05, 31 Aug 2004 (UTC)

 * It looks OK (apart from the castrated ram in the second para). However, I think the subject could do with a bit of explanation about origins, because 'Alphabeticisms' and 'Initialisms' came first, at about 1899, and 'Acronyms' came along later (1940s).  There are a whole bunch of other words to discuss various abbreviations and contractions which need to be put into context as well.
 * Looking around, ISO 1087:1990 Section 5.2.2 describes all these sorts of things and how they should be used as science terminology, and both acronym and initialism are deprecated in favour of 'abbreviated form'.
 * I also asked at a meeting I was in today (seven other people), and just got blank stares when I mentioned initialism.
 * By the way, when do you start your campaign to change TLA to TLI?  Noisy 16:19, 31 Aug 2004 (UTC)
 * Perhaps your meeting says more about the circles you live in than the knowledge of the word… anyway. The object of an encyclopedia is to inform, not to decide use. Informing people about the standard definition of acronym, and the existance of initialism as a category of abbreviations, is important here. If encyclopedias only propagated common errors and left out information which adds on already present knowledge, they would not be worth keeping. Anárion Talk 17:35, 31 Aug 2004 (UTC)
 * By the way, I believe TLA stands for Three Letter Abbreviation, so what needs to be changed? Anárion Talk 17:53, 31 Aug 2004 (UTC)
 * "three letter acronym": 12,200 Google hits.  "three letter abbreviation":  7000 Google hits. I have 25+ years as programmer/designer/analyst in the software industry, and this is the first place that I have heard of initialisms.  Your point? Noisy 08:02, 1 Sep 2004 (UTC)
 * I have never heard of BEP (random page). Your point? Anárion Talk 08:09, 1 Sep 2004 (UTC)
 * This is better, however:
 * I don't think it is necessary to bore the reader with the details of the dispute in the first section of the article. In my version, I moved the details of the dispute to a separate section.
 * Your use of the word "strict" to describe your definition of "acronym" is POV. The implication is that my definition is "not strict" or "lax", when in fact it is just as "strict" (=exact, precise), just different. The word "strict" is inherently biased and should be avoided. I think the adjective "exclusionary" (=of or related to the act or an instance of excluding) more neutrally describes your definition because the objective difference between the definitions is that your definition excludes many abbreviations in the category "acronym" that mine includes.
 * The discussion about abbreviations like JPEG is incorrect. The term "portmanteau acronym" is not used in the way you suggest: all of the Google hits refer to acronyms (or initialisms) that are made up of other acronyms that have been fused together by a shared letter. This is a new phenomenon for me, and I think it should be covered in the article, but the way you describe "portmanteau acronym" does not match what people actually use that phrase for. Indeed, every one of the Google hits for "portmanteau acronym" are examples of what you would class initialisms and not acronyms. Yet more evidence that your definition does not reflect the reality of usage...
 * By actively excluding the list of acronyms that you don't count as acronyms, you are subtly pushing your POV. I think it is far more NPOV to include them, but mark that their status as acronyms is disputed, as is the case in my version.
 * Nohat 17:28, 31 Aug 2004 (UTC)

 * Main reason for moving it up was to get rid of duplication: I would rather just define acronyms in the top paragraph, and only mention the confusion some people have about the term later on, but that could conceivably by you seen as "POV pushing". Perhaps a split is needed there.
 * "Strict" is a word I used because there is no single word to describe acronyms, if initialisms are also called acronyms. "Classical" is perhaps better here.
 * Portmanteau acronym is a leftover from the original article. If you know of a better word, let me know.
 * Including the list of initialisms in an article on acronyms is subtly pushing the POV that initialisms are acronyms. Plus it further defeats the need for a separate "initialism acronym" article. Anárion Talk 17:35, 31 Aug 2004 (UTC)

 * Again, you continue to ignore the fact the the preponderance of usage points to "acronym" being used in the way I describe, and you provide no reason why we should reject this definition other than the circular argument that it is "wrong". Even though it has been shown that many people, even authors of published books, use "acronym" in the way I describe, please explain why this definition should be rejected, especially considering that you haven't shown any reason why we should reject the principle that the only arbiter of English usage is usage itself. Nohat 23:33, 1 Sep 2004 (UTC)
 * Nohat, you seem to be missing one fundamental point: just because "most people"(assuming that is even the case) do something does not make it right or acceptable. If we went by the "most people" rule, the possessive of 'it' would be 'it's', and 'flout and 'flaunt' would have the same meaning. Sentences such as "She was friendly, outgoing, and had an endearing smile" would be perfectly correct English. (This last grates me more than all others, because it seems even the best writers do not know how to deal with verb phrases.) I also encourage you to consider that, if you say "most people", and you do not have data to presume such, this whole thing falls under the original research clause. Having read through all this discussion, I think you lose. You sound like the religious right fending off evolution - it's not the facts, but the bigger voice which wins. Suffice it to say I will not be hanging around here for any bons mots - my observation, and don't bother to correct me if I'm wrong - is that several people have attempted to reason with you, but it's your way or the highway, as we like to say in the colonies. Denni ☯ 02:42, 2004 Sep 2 (UTC)

 * BTW (that would be an initialism, BTW), just as a side note to the first comment on this talk, my Oxford Dictionary of Current English has the derivation of acronym as Greek, from acron, end and onoma, name. That is to say, the name you get at the end, not the group of three, or four, or five letters spit out. That would be an initialism. Denni ☯ 02:52, 2004 Sep 2 (UTC)

 * Are you so afraid of your points that you refuse to argue against anything I might say in response?

 * Your analysis betrays a fundamental misunderstand about how language works. Your statement " just because "most people" (assuming that is even the case) do something does not make it right or acceptable" is exactly wrong. The rules of language are not handed down from on high by some priesthood of language masters. On the contrary: the rules of language are set by how language actually works. Linguistics, the study of language, has been in agreement on this point for a very long time. If you talk to people who actually study language as their profession you will find universal agreement that the very concept of prescriptive rules is fundamentally flawed and not in any way a reflection of how language works. Because linguistics is not a large field—it takes a person of certain demeanor, not to mention caliber to undertake the study with any degree of scientific rigor—there are not many people who are able to explicate the admitedly complex ideas that form the foundation of my points. On the other hand, it is no surprise that self-appointed "experts" on English who have no understanding of linguistics are willing to espouse their uninformed, facile views about how they think language should work, without having any real experience with scientific analysis of language.

 * You and the others continual make an appeal to authority by quoting dictionary defintions, but I would think it would be obvious then when you make such an appeal you have to provide a justification as to why your authority should be believed. As I have explained over and over and no one has been able to refute, the only arbiter of English usage is usage itself, not flawed interpretations of entries in outdated and imperfect dictionaries. No one as of yet has provided any reason why the fact that many people use "acronym" in the way I describe should be labeled incorrect other than by begging the question and just declaring it incorrect.

 * And the sentence "She was friendly, outgoing, and had an endearing smile" is perfectly idiomatic English and only a tireless pedant who seeks to wedge formal logic into the infinitely illogical world of language would contest that. People say and write English sentences like that all the time and the world hasn't imploded because your precious rules of parallel structure have been violated. Language works in illogical ways and that doesn't make it "wrong". All the people who have told you otherwise were simply mistaken. Furthermore, your appeal to consequences that going by the "most people" rule would lead to a irrevocable degeneration of language is such an old, trite, and trivial misunderstanding of how language change works that it's almost always covered and refuted in any introdutory linguistics class.

 * In sum,
 * The only arbiter of English usage is usage itself. Neither dictionaries, usage guides, nor self-appointed "language experts" have any authority over deciding what is and isn't "correct" English. "Correct" English is defined only by the preponderance of usage. This is how language has always worked, and is how it will continue to work, regardless of how many "language experts" try to stop it.
 * The evidence shows that many people—perhaps not a majority, but certainly a significant number—including authors of published books, use the word "acronym" to describe abbreviations like FBI.
 * When a large number of people use a word to mean a certain thing, that certain thing becomes one of the definitions of the word. "Broadcast", for example, used to be only a farming term describing a method of distributing seeds into the ground. When the newer meaning relating to mass media came into use, it is doubtless that there were those who protested this encroachment on the meaning of a valuable farming term. But, as always, the pleas of the protesters were ignored by the users of the language and both meanings of "broadcast" are used by everyone. No one in their right mind would protest the new meaning of "broadcast" today, and I imagine that in the near future, when more dictionaries follow Merriam-Webster's suit and include the meaning of "acronym" that includes abbreviations like FBI, those who protested that definition, such as yourself, will be looked upon with mild amusement if not scorn, much as we look upon those who protested the new meaning of "broadcast". The tides of usage flow only in one direction: towards continual change.

 * Finally, my suggestion would be for those who think I'm wrong to spend some time learning about how language works from a scientific perspective, and then come back and argue. Until then, I'm getting tired of battling people who don't even know the first thing about the realities of linguistics. Nohat 04:53, 2 Sep 2004 (UTC)

 * Nohat, your hostile attacks on anyone who refutes your claim that initialisms ARE acronyms are making it extremely difficult to work out a resolution. Please consider that YOUR usage is not necessarily standard usage, and just because you believe you are correct does not make it so. Anárion Talk 07:44, 2 Sep 2004 (UTC)

 * What's making it difficult to work out a resolution is not my alleged hostile attacks, but your refusal to discuss the core issue at hand. You make the presumption that there is such a thing as "standard" or "correct" usage, and this is an assumption that I and all linguists reject. Until you can provide an explanation as to why there is such a thing as "correct" usage and what it is, and who defines it, the argument about what "standard usage" of the word "acronym" is is moot. I have asked now, at least 3 times, for you or anyone to give a reasonable reason as to why we should accept the notion of "standard" or "correct" usage that is not based on actual usage, and no one has even attempted. Nohat 08:07, 2 Sep 2004 (UTC)

 * I've read Acronym/temp and Acronym/temp2, both are superior to the current article, but I think Acronym/temp gives a better indication of usage and meaning. I'd reccomend immediately changing the article, and letting it continue to evolve from there. — siro  χ  o  05:42, Sep 2, 2004 (UTC)

 * /temp (Nohat's version) has the fatal flaw it treats all initialisms as if thet were acronyms, and treats the correct view as if this is a mistaken minority view. To use Nohat's favourite initialism: that is not NPOV, and unacceptable. My version takes the opposite view: acronyms are defined as they are, but the curious fact some people call initialisms and acronyms alike "acronym" is discussed. 07:44, 2 Sep 2004 (UTC)

Sorry to intrude on private grief: to add my twopennyworth, I'm a speaker of British English, and I'd never heard of an initialism before reading this discussion. Having been enlightened, I accept that there is a useful distinction to be drawn, but general usage in my experience (IME) is to ignore this technical distinction and call any contraction formed from initial letters an acronym, whether pronounced as a word (NATO or OTAN) or not (FBI) or combination (JPEG). The article ought to explain the techincal difference, but also point out the common usage. If there is a serious difference of views, then the article ought to explain that too.

Of the options, I prefer Acronym/temp2, but either is much better than the protected article. -- ALoan (Talk) 10:12, 2 Sep 2004 (UTC)

As someone who studied applied linguistics at postgrad level, I'd have to say that initialism is a semi-technical term used in the literature but not found in common usage. And usage is what counts, even in an encyclopaedia. The term Initialism forms a useful distinction for the professional linguist, but not for the general reader (who, I imagine, is the target audience here) and should be covered in the article as being the technical name for a subset of those forms that are commonly known as acronyms. And having a section in the article discussing a 'dispute' that is happening on the article talk page is just one of the more blatent examples I've seen of Wikipedia disappearing up its own fundament. Take it out altogether!145.36.24.29 15:02, 2 Sep 2004 (UTC)

 * Do you mean as in In the classical definition the term acronym is reserved to abbreviations which can be pronounced as words (e.g. NATO), but the term acronym is by some extended to include the similar initialisms, which are instead pronounced as a series of single letters (e.g. HTML). and There is debate over wether the word acronym can be applied to any set of initials. One view is that any abbreviation formed out of the initials of the contained words is an acronym, regardless of wether or not the abbreviation can be pronounced as a word. Under this definition initialisms are not a distinct type of abbreviation, but rather a subset of acronyms. This definition has no word to refer to acronyms which are not initialisms. The opposite view is that abbreviations like "BBC" and "IBM" cannot be pronounced as single words, and therefore are not acronyms. Under this more exclusionary definition of "acronym" initialisms are a distinct category of abbreviations, and there is no single English word to describe both types of abbreviation. ? (from Acronym/temp2 Anárion Talk 07:40, 3 Sep 2004 (UTC)

 * Yes. This is not a real world dispute, it is a dispute on this page only. This habit of writing articles as if the concerns of the editors were more important than simply presenting the facts to a non-specialist readership (which is, after all, the function of an encyclopaedia) is one of the key reasons why Wikipedia is still a long way short of being as useful as any of the best available print reference works. 145.36.24.29 08:29, 3 Sep 2004 (UTC)

 * So you dispute that the word initialism is used to describe initialiams, and some people call these also acronyms, is a fact? Anárion Talk 08:59, 3 Sep 2004 (UTC)

 * No, I dispute that the dispute is a fact anywhere other than on this talk page. I have never come acros it as a dispute among linguists in the literature. I also dispute the (implied or otherwise) assertion that 'initialism' is a term in common usage among what might be tremed the 'general reader'. 145.36.24.29 09:18, 3 Sep 2004 (UTC)

 * It is false to claim that the dispute is unique to this page. First, the various dictionary definitions don't all agree, for example the Merriam-Webster and the OED. Second, there is definitely evidence that this dispute exists on the internet outside of Wikipedia. For example:, and particularly in the discussion of the "acronym" and "abbr" HTML elements: . Many more examples can be found by Googling for "acronym vs initialism". So, claiming that this dispute is somehow unique to this page and is therefore not worth mentioning in the article is patently false. Nohat 18:11, 4 Sep 2004 (UTC)

 * Oh, I also dispute there is a dispute: Nohat is the first person I have come across who insists unprouncable abbreviations can be acronyms. Anárion Talk 09:37, 3 Sep 2004 (UTC)

 * Then I'm the second. 145.36.24.29 09:44, 3 Sep 2004 (UTC)

 * I am a third, and I think there are others above. -- ALoan (Talk) 11:45, 3 Sep 2004 (UTC)

 * So we agree there are people who use initialism, and people who don't. Anárion Talk 11:51, 3 Sep 2004 (UTC)

I have three different dictionaries (one new Macquarie, one new Webster's, and one very old Australian Oxford) in my house, and none of them even have 'initialism' as a defined term. But all three define 'acronym' simply as "a word formed from initials of other words". I don't see why we should be forced into following in our article a distinction that is only made by the Oxford English Dictionary. - Mark 03:20, 3 Sep 2004 (UTC)

 * As has been pointed out somewhere on this page, the distinction is not unique to the OED, but in common use among those who know what they're talking about. Anárion Talk 07:40, 3 Sep 2004 (UTC)

 * But this article is not written for that audience. 145.36.24.29 08:29, 3 Sep 2004 (UTC)

 * But an encyclopedia should be written for everyone, not just any one hypothetical "audience". Anárion Talk 08:59, 3 Sep 2004 (UTC)

 * Yes, but it should be addressed primarily at the general reader, with sufficient technical information to be useful to the specialist too.

 * We need to reach a consensus. Would it help to crystalise matters if we had a vote on the two temp pages (either of which, I think we agree, is significantly better than the current page) with comments for and against both of them? -- ALoan (Talk) 11:45, 3 Sep 2004 (UTC)

 * I still fail to see what is apparently unacceptable about defining acronyms as acronyms, with a note that some people also call initialisms acronyms. This should make both the "initialisms exist" and the "all abbreviations formed from initials are acronyms" crowd happy, right? Anárion Talk 11:51, 3 Sep 2004 (UTC)

Back to left margin - yes, as it happens, I agree that Acronym/temp2 (i.e. your version) is better (I said so above yesterday) but I also think we need to reach a consensus. Excuse me for saying so, but you and Nohat seem to be rather entrenched, and I think it would help to take a straw poll of how others see the issue. I'm only trying to help ;) -- ALoan (Talk) 12:25, 3 Sep 2004 (UTC)

 * Yes thanks, I appreciate the help. Nohat and I are not able to reach consensus apparently. Feel free to edit /temp2 by the way. Anárion Talk 12:27, 3 Sep 2004 (UTC)

 * As a pretty "neutral" outsider (I added only the "ichthys" Greek example, and it is pretty much not involved in this dispute) can I offer my take on what is being said, and make a stab at resolution?

 * (I won't wait for an answer...) We have some editors who are very adamant about the distinction between "acronym" and "initialism", and who are supported in their view primarily by the OED. We have others who are very adamant that an "initialism" is only a type of acronym; primary support for this view comes from Merriam-Webster, and anecdotally from Google.

 * What about an introductory paragraph like that in Acronym/temp3? We thus identify where the typical usage of "initialism" comes from, and we can include some discussion of them in the acronym article itself (where the average Net user expects them to be, based on the anecdotal Google evidence). On the initialism page, we would need to mention that American usage, and indeed the most common usage, does not distinguish them from acronyms or considers initialism to be a subset of acronyms.

 * For the record, I am American, and have only heard (better "read", as I have never literally "heard" the term) the term "initialism" in very specialized discussions. If the term is is common usage in British English, for instance, a slight change to my introductory paragraph would be in order.

 * Of the other options presented thus far, I think that Acronym/temp2 is better; however, for some (perhaps many, yea even most, though I have no hard evidence about percentages there) readers, the distinction is not helpful for them finding the information they need. (I.e. mentioning the distinction is very useful, but hiding the information on a large part of what the layman considers an acronym in another article is not.) For the professional, we provide that information a second time, perhaps in greater detail under initialism, which is linked from acronym.

 * Here's hoping that this was helpful and didn't just muddy the waters more... Mpolo 02:24, Sep 5, 2004 (UTC)

 * On the contrary, a voice of reason. I still see no reason why this 'dispute' is covered in the article. Bmills 11:29, 6 Sep 2004 (UTC) (otherwise known as [User:145.36.24.29|145.36.24.29]])

 * It is very helpful indeed. I have revised /temp2 based on your suggestions. Anárion Talk 17:05, 6 Sep 2004 (UTC)

From the village pump
I ask that those who have formal training in linguistics pay a visit to Talk:Acronym and try to help me explain how if a large number of people use a word to mean a certain thing, then that certain thing is therefore a legitimate meaning of the word. I have been trying for several days to get this point across, but many people seem to be laboring under the mistaken belief that the only valid meanings of words are those that are set down by the Oxford English Dictionary. Nohat 04:58, 2 Sep 2004 (UTC)
 * More accurately: should, as Nohat wishes, the distinction between initialism and acronym be completely obscured, or should acronyms be defined as they are defined in dictionaries, with a note that some people also call initialisms "acronyms"? Anárion Talk 11:39, 2 Sep 2004 (UTC)

 * As you (Nohat) point out, only a lilliputian minority of people call acronyms (or a subset thereof) "initialisms", and you've already namechecked the prior (martial) art: descriptive v prescriptive grammar.

 * God's primary source for the "initialism" usage appears to be... er... Wikipedia.

 * chocolateboy 01:30, 3 Sep 2004 (UTC)

 * This Nohat drove me away from the article with his insults and intransigent attitude after I courteously tried to open a discussion on the talk page (rather than simply correcting the article without notice). It was a very unpleasant experience, and I am not here for that.  That's why I dropped out from Wikipedia for more than a year.  I don't want to drop out again, so I am glad others are in there working him over.  He seems to think it is his article.

 * It is pernicious to wilfully confuse technical terms in the way he seems determined to do. I will not participate further, but you are welcome to see my description of the problems of the article (and his responses, judge for yourself) on the talk page.

 * I assure you (as I did him) that I am no prescriptionist, quite the contrary, I firmly believe you cannot hold back the tide, but, as for technical terms, used to sort out technical meanings, precision (not prescription) is still the requirement. If everybody in the world confused a squid with an octopus, and a great many do, it would not matter, it would still be wrong.  Usage rules in the long run, of course, but it is the duty of a reference work to try to make things clearer, not more confused.  Looking things up in dictionaries does not make you a prescriptionist.  There is no modern prescriptionist dictionary, they are all descriptive, as is every linguist. Insisting on the undiscussable correctness of one's own opinions, now that's prescriptionist.    Ortolan88 02:30, 3 Sep 2004 (UTC)

 * I dispute the mistaken notion you and Nohat apparently share that initialism is a neologism. The word initialism dates from the late nineteenth century. Acronym pops up in main common usage only in the early 1940s. Also note that originally acronyms were a subset of initialisms, and certainly only had the strict meaning: initialisms which could be pronounced as a word (NATO), rather than a series of letters (FBI). At some point it seems some people began calling ALL initialisms acronyms, at which point initialism was restricted in meaning to 'acronyms which cannot be pronounced as a word'.
 * As Ortolan88 above I also note that Nohat's insults and his generally intransigent attitude over "his article" are the major problem here. Except for Nohat all contributors seem reasonable and wiling to work out a compromise. Anárion Talk 14:00, 3 Sep 2004 (UTC)
 * By the way, Nohat vs reason ;-) (not intended to be taken seriously!) Anárion Talk 14:03, 3 Sep 2004 (UTC)

I'm unaware of the dispute in process, but according to current dictionaries there is a simple, clear distinction between "acronyms," which are pronounced as single words (examples given by AHD4 are WAC, and radar), and initialisms, which are pronounced letter-by-letter (e.g. WPA, IRS, TNT, ESP). There's nothing hard to understand about that. All modern dictionaries profess to report meanings and spellings on the basis of frequency of usage. Referring to initialisms as acronyms is not a "meme on the rise," it's just imprecise. It is frequently a subtly disrespectful usage; people who don't understand the actual terms and believe they are intentionally obscurantist propellerhead jargon show their feelings by not bothering to use the proper terms for the terms themselves; that is, people who aren't interested in what TCP/IP is, are not likely to be interested in the metadetail that TCP/IP is an initialism rather than an acronym. [[User:Dpbsmith|Dpbsmith (talk)]] 14:11, 3 Sep 2004 (UTC)

 * Exactly! Finally someone who understands :) Anárion Talk 15:33, 3 Sep 2004 (UTC)

 * For the record, I don't think initialism is a neologism. I don't think I share anything with Nohat.  For one thing, I have lots of hats.

 * Nice to see that other people think the distinction between initialism and acronym is understandable and worth keeping. On the Talk: Acronym page I point out that the article is also hopelessly confused about portmanteau words and suggest anagrams as another category of words made from words Ortolan88 16:43, 3 Sep 2004 (UTC) PS - I do wish people would indent these discussions.  This is my left margin.
 * No doubt the distinction exists and is correct, but the common perception of acronym should be alluded to and explained. — siro  χ  o  17:20, Sep 3, 2004 (UTC)

 * Yes, with acronym the name of the game is pronounceability as if it were a normal noun. UNESCO, OPEC, and NATO spring to mind here. Dieter Simon 23:49, 3 Sep 2004 (UTC)

Nohat's actual view
As clarified on Village pump:

 * 1) I never claimed "initialism" is a neologism. Indeed, the OED says it's an older word than acronym, and has quotations to prove it. I only claimed that it's a rarely-used word, and I think that is borne out by the evidence..
 * 2) At least one major dictionary supports my view of the definition of "acronym": Merriam-Webster. Part of its definition of "acronym" says "an abbreviation (as FBI) formed from initial letters : INITIALISM", and its definition of "initialism" says, in entirety, "an acronym formed from initial letters". The dictionary clearly makes the case here that initialisms are a subset of acronyms.
 * 3) There is substantial evidence, delineated on Talk:Acronym, that the meaning of acronym that includes abbreviations like FBI, is in substantial use, not only online, but in published books. Published books are vetted not only by their authors, but by editors and publishers, and because so many examples of the word being used this way have crept their way into published books, it seems disingenuous to claim that this meaning of the word is only used by ignorants and the uneducated.
 * 4) My opponents have continually claimed that I am attempting to "obscure" the distinction between initialisms and acronyms or that I believe that the distinction is not worth keeping. This is false. My claim is that initialisms are a subset of acronyms, as Merriam-Webster explains; not that they are the same set.
 * 5) My opponents have claimed that I am trying to insist that my definition is the only correct definition. This too is false. Every version of Acronym that I have supported has included the information that some people and some dictionary definitions support the view that initialisms that aren't pronounced as words aren't acronyms. My only aim is that the article on acronyms treat the two definitions equally and not assert that one or the other is correct. This is what I have attempted on Acronym/temp. There are two competing definitions of "acronym". Both are supported by dictionary definitions. Both are supported by usage in published books and on the web, and I don't see any valid reason why both shouldn't be treated equally on Acronym.

Nohat 18:00, 4 Sep 2004 (UTC)

Acronym/temp and Acronym/temp2
I think that, despite the acrimonious debate that ensues, both User:Anárion's and User:Nohat's (my) versions are slowly reaching a consensus. I have recently made major changes to Acronym/temp that I encourage everyone to consider. In particular, in the dispute section, I have made an attempt to motivate the conflicting views over acronym in a NPOV way, describing the traditional definition as traditional—at this point I am willing to concede that the meaning of "acronym" that excludes abbreviations like FBI may be older and more traditional. I state that there are numerous examples of both meanings being used in published works.

I also agree that Anárion's version has improved, and think that the major assertions in the competing versions are converging. I think that the basic assertions made in my "dispute" section are the same as those in Anárion's "initialisms as acronyms" section.

The reason I advocate my version at the moment however, is because I still have a few quibbles with Anárion's version.

I think that titling the section on the dispute "initialisms as acronyms" is a little misleading. Why don't we just call a spade a spade and title the section "dispute", as I have, or something like "dispute over the defintion", or "conflicting defintions". The title "initialisms as acronym" is, I'm sorry to say, a suble push of the traditionalist POV in that it makes the assumption that "initialisms aren't acronyms", which is the core of the debate. Despite the misconceptions some of the other posters have had that this dispute is somehow unique to Wikipedia, there is plenty of evidence that this very issue has been discussed and argued elsewhere. Of course, nowhere else can the outcome of that argument claim to be neutral, as the dénouement of this argument hopefully will be. It is better not to make the assertion that the traditional definition is more correct, but simply to declare that some people believe that. I think it is equivalent to my calling the section "acronyms that aren't acronyms".

Similarly, in the first paragraph, the traditional view is described as the "classical definition", giving it more weight than the newer view, which is merely ascribed to "some people". Again this is a subtle POV push that the traditional definition is "better". It would be more neutral to describe both views using analogous terminology by stating that the status of certain abbreviations is disputed, without making the claim that they are or aren't acronyms.

Also, in the examples section, by not including examples of the disputed forms, it is pushing the POV that the traditional definition is correct. In my version, I have revised this section to clearly indicate which are traditional acronyms, and which are disputed acronyms, without actually excluding them.

In all, despite the splenetic rhetoric, I think that we have made substantial progress on reaching a consensus. If Anárion can address these few remaining issues, then I think we will reach a point where we can merge the competing versions and unprotect the main page. I hope I have addressed any remaining concerns. If not, let me know what about my version you disagree with, and I hope we can work it out.

Nohat 19:15, 4 Sep 2004 (UTC)

 * Your points have been adressed in Acronym/temp2 — are you agreed then it can replace the old article, so the "dispute" can end? Anárion Talk 17:35, 7 Sep 2004 (UTC)

 * I prefer the new Acronym/temp2 as well, because "dispute" conjures images of dozens of people up in arms about the usage of the term, and I honestly don't believe that that's the case here. There is a dispute among Wikipedia editors, but not in the wider world, so to speak. I don't think that there's anybody who would leap to his feet in a linguistics convention and cry out, "That's not an acronym, you nimwit, that's an initialism!" (or vice versa). -- Mpolo 19:47, Sep 7, 2004 (UTC)

Ending the dispute
Is there any opposition to making /temp2 into the article? All objections to it would seem to be resolved now. Anárion Talk 15:19, 9 Sep 2004 (UTC)
 * I wouldn't go so far as to say that all objections are resolved, since I still object to the use of "Many, including" to start the second sentence. I have still not found a single person who has even heard of initialism, so I think it is craven to include that phrase.  Let me put this in context: next month I will have been working in the computer industry for 25 years, and in that time I and my colleagues have used acronyms on every single one of those working days.  On the odd occasion I actually form sentences where over half the words are acronyms! I have created numerous glossaries and acronym lists, and no-one has ever corrected me.  I am by nature a pedant, (which is why I irritate my colleagues by using '-ize' rather than '-ise', as Fowler recommends), so if I had found that initialism was the correct form, then I would have adopted it.

 * All that said, my research bears out that initialism was the original usage from 1899, and that acronym was introduced in the 1940s to give a name to initialisms that could be pronounced as a word (as opposed to spelling out the letters). However, having surveyed a number of dictionaries, the OED stands pretty much alone in even mentioning initialisms, let alone giving a meaning of spelling out the letters (which doesn't seem to have been the original intent of the word when it was created): it seems that common usage will win out in the end, with professional linguists fighting a losing battle.  Alphabeticism doesn't seem to get a look in.  The only saving of initialism is likely to be with the debate over ISO 1087:1990, where confusion over the and tags seems to have forced the powers that be to give up and just use . I have seen it pointed out that this may cause confusion for speech interpreter programs, because an abbreviation like 'Mr' should be pronounced 'Mister'; 'radar' should be pronounced 'radar'; FBI should be pronounced 'eff bee eye'; 'JPEG' should be pronounced 'jay peg'; and 'SAT' could be pronounced either as 'sat' or 'ess ay tee' depending on context.  Bad luck for the blind community.

 * Temp2 is a much better starting point (now that Poccil has eliminated the castrated ram). There will still be work to do, but I think things are a lot clearer now.  [[User:Noisy|Noisy | Talk]] 17:37, 9 Sep 2004 (UTC)

 * Thanks. You are, of course, quite correct on the initialism/acronym change-in-meaning, and this (complete with perhaps other points) should still be addressed, but I feel this should be done in the main article 'acronym' and not in multiple competing temp versions. About the HTML tag: that merits mentioning in the article, as it strengthens the point that the term acronym has become dilluted in meaning since the 1940s. Anárion Talk 17:43, 9 Sep 2004 (UTC)

 * "Many" is certainly a "weasel word" in Wikipedia parlance, but I don't think it is going to be possible to avoid some squirming there. There obviously exist persons that use this word (User:Anárion comes to mind), but it's kind of hard to judge just how many. Google hits for "initialism" tend to be the Wikipedia article or mirrors of it, at least in the first 20. It also shows up on a "hacker" message board, with someone vehemently defending that IBM is no acronym. Do you have a suggestion to better reflect all points of view? (We might soften "many" to "some", though that's still weaselly...) .. Mpolo 17:52, Sep 9, 2004 (UTC)

 * Hmm. What about "Primarily in professional linguism, people further distinguish (etc.)"? I could live with that, and should avoid "weasel words" Anárion Talk 18:01, 9 Sep 2004 (UTC)

 * I like it. If there is no complaint after about a day, I would say to go ahead and replace the page with /temp2 with that change. There will probably still be some changes to make, but it's a much better base, I believe. -- Mpolo 18:59, Sep 9, 2004 (UTC)

I'm not clear how the idea that "professional linguists" are the ones who prefer the traditional definition got in here. As I explained before, if you actually ask linguists, what you'll find is that they defend definitions that reflect actual usage. Indeed, any "linguist" who takes a prescriptive view of usage could hardly be called "professional".

Ascribe the insistience of usage to those who actually insist upon it: prescriptive grammarians. Nohat 05:14, 10 Sep 2004 (UTC)

 * Nohat, please don't start this again. Despite what you think, initialism is not reserved to pedantic, prescriptive grammar geeks. Do you have any real objections, and suggestions on how to change them? Anárion Talk 07:31, 10 Sep 2004 (UTC)

 * You misunderstand me. My objection is that there isn't any evidence that "professional linguists" are the ones who use the word this way. Show me some evidence that they do, or reword it. Nohat 17:01, 10 Sep 2004 (UTC)

 * So what do you, guardian of the Nohattian err "English" language, recommend instead? Surely you cannot still believe initialism is used by nobody. Anárion Talk 17:06, 10 Sep 2004 (UTC)

Well, I've changed my tune somewhat since I entered this debate, so I did a Google on 'lingistics initialism' and came up with the following examples: Swedish (?) source another international source old (1994) Linguitics discussion thread PDF file (dissertation ?) blog reference to 'Penguin Dictionary of English Grammar' University of North Carolina course exercise by Mark Canada - the Professor of English

Most of those seem to be of an academic bent, rather than related to common usage. If these don't fit the bill, I'll carry on working through the 533 hits. I am now really confused. I'm going to buy the latest Fowler's at the weekend: mine is only the second edition. Perhaps that will clear things up. [[User:Noisy|Noisy | Talk]] 17:57, 10 Sep 2004 (UTC)

I think the phrase "Primarily in professional linguism" is unacceptably overstating the case. The distinction between acronym and initialism is expressed in ordinary definitions in some ordinary desk dictionaries, such as the one that is within arm's reach of me as I write. Desk dictionaries are not tools for professional linguists. It's just a case of precise usage versus loose usage. Note, too, the closely related word "acrostic," "A poem or series of lines in which certain letters, usually the first in each line, form a name, motto, or message when read in sequence." A random series of letters is not an acrostic, nor is it an acronym, except in loose usage. Some authorities consider it acceptable loose usage, some do not.

Another random data point is that if you search on Amazon for "dictionary of acronyms," you will find that there are very few books which are simply "dictionaries of acronyms." Most of them are split, roughly half-and-half, between "dictionary of acronyms and abbrevations" and "dictionary of acronyms and initialisms." This confirms my belief that precise usage restricts acronyms to mean only pronounceable combinations. It of course leaves open the question of whether people who are not "professional linguists" care about precise usage. [[User:Dpbsmith|Dpbsmith (talk)]] 13:41, 11 Sep 2004 (UTC)

 * Indeed it is entirely the other way around. Only those people who are not "professional linguists" care about precise usage. Professional linguists tend to concern themselves mainly with how words are actually used, not with how people think they ought to be used. The idea that it is professional linguists who would insist upon one meaning of a word and not another is just wrong. It is an entirely separate group that concerns themselves with such things and it is simply a misrepresentation to associate that kind of behavior with linguists. As I explained above, the name for that group of people is grammarians, in particular, prescriptive grammarians. Nohat 22:26, 11 Sep 2004 (UTC)

 * So, by your logic, "prescriptive grammarians" are not linguists? Anárion Talk 22:30, 11 Sep 2004 (UTC)

 * That is correct. A linguist is a person with a degree in linguistics, or at least some linguistic training, who studies how language works, not someone who makes pronouncements of how language ought to work. See Linguistics Nohat 03:43, 12 Sep 2004 (UTC)

 * So you see yourself as a "prescriptive linguist" then? Can you give any constructive criticism as to how to rephrase the sentence? Anárion Talk 11:54, 12 Sep 2004 (UTC)

 * Could we say something like this:

 * A further distinction is sometimes made among grammarians and other students of language between acronyms that can be pronounced as a word (e.g. NATO) and those that cannot (e.g. HTML). The latter category may be termed initialisms.

 * We remove "professional linguist" in favor of grammarians and students of language. We weasel in a "sometimes" to indicate that it is not universal, but we keep the distinction in the article, as is currently done in /temp2. Is that acceptable to all? -- Mpolo 12:34, Sep 12, 2004 (UTC)

 * I've rephrased it as:
 * The term is often further restricted to abbreviations which can be pronounced as words (e.g. NATO). Abbreviations which are instead pronounced as a series of single letters (e.g. HTML) are classed as initialisms.
 * Primary reason is that not only grammarians and language students use the term initialism. Anárion Talk 12:37, 12 Sep 2004 (UTC)

Silly question
Standard (Attic) Greek for "name" is onoma, not onyma, which is Aeolean or Doric. Is it worth noting that this is Aeolean/Doric in the etymology line, or should we leave well enough alone. Mpolo 19:12, Sep 12, 2004 (UTC)

 * What is the form in classic Greek? (Or is that "Attic Greek"…) Anárion Talk 19:50, 12 Sep 2004 (UTC)

 * Attic is usually considered to be "the" classical Greek (primarily because 95% of the authors anyone reads wrote it -- it was the dialect of Athens). Most classical dictionaries consider the other dialects only as cross-references to the Attic form -- mine had onyma, onymazw, onymainw Aeol. and Dor. for onom-. Attic was the basis that developed Koiné (Biblical Greek) and Demotic (Medieval Greek), and ultimately Modern Greek. After checking, I see that the dialect "Aeol." is called "Aeolic", not "Aeolian". -- Mpolo 07:26, Sep 13, 2004 (UTC)

 * Thank you. I find it rather interesting… should merit a note in the article. (Perhaps instead of Greek, Aeolic/Doric Greek ?) On the other hand this may unnecessarily clutter the sentence. Anárion Talk 07:33, 13 Sep 2004 (UTC)

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

title: Talk:Acronym/Archive 3


text:
Axiom of choice

In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty sets is non-empty. Informally put, the axiom of choice says that given any collection of sets, each containing at least one element, it is possible to construct a new set by choosing one element from each set, even if the collection is infinite. Formally, it states that for every indexed family $$(S_i)_{i \in I}$$ of nonempty sets, there exists an indexed set $$(x_i)_{i \in I}$$ such that $$x_i \in S_i$$ for every $$i \in I$$. The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem.

In many cases, a set created by choosing elements can be made without invoking the axiom of choice, particularly if the number of sets from which to choose the elements is finite, or if a canonical rule on how to choose the elements is available — some distinguishing property that happens to hold for exactly one element in each set. An illustrative example is sets picked from the natural numbers. From such sets, one may always select the smallest number, e.g. given the sets {{4, 5, 6}, {10, 12}, {1, 400, 617, 8000}}, the set containing each smallest element is {4, 10, 1}. In this case, "select the smallest number" is a choice function. Even if infinitely many sets are collected from the natural numbers, it will always be possible to choose the smallest element from each set to produce a set. That is, the choice function provides the set of chosen elements. But no definite choice function is known for the collection of all non-empty subsets of the real numbers. In that case, the axiom of choice must be invoked.

Bertrand Russell coined an analogy: for any (even infinite) collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate collection (i.e. set) of shoes; this makes it possible to define a choice function directly. For an infinite collection of pairs of socks (assumed to have no distinguishing features), there is no obvious way to make a function that forms a set out of selecting one sock from each pair without invoking the axiom of choice.

Although originally controversial, the axiom of choice is now used without reservation by most mathematicians, and is included in the standard form of axiomatic set theory, Zermelo–Fraenkel set theory with the axiom of choice (ZFC). One motivation for this is that a number of generally accepted mathematical results, such as Tychonoff's theorem, require the axiom of choice for their proofs. Contemporary set theorists also study axioms that are not compatible with the axiom of choice, such as the axiom of determinacy. The axiom of choice is avoided in some varieties of constructive mathematics, although there are varieties of constructive mathematics in which the axiom of choice is embraced.

Statement
A choice function (also called selector or selection) is a function f, defined on a collection X of nonempty sets, such that for every set A in X, f(A) is an element of A. With this concept, the axiom can be stated: $$

Formally, this may be expressed as follows:

 * $$\forall X \left[ \varnothing \notin X \implies \exists f \colon X \rightarrow \bigcup_{A\in X} A \quad \forall A \in X \, ( f(A) \in A ) \right] \,.$$

Thus, the negation of the axiom may be expressed as the existence of a collection of nonempty sets which has no choice function. Formally, this may be derived making use of the logical equivalence of $$\neg \forall X \left[ P(X)\to Q(X) \right]$$ to $$\exists X \left[ P(X)\land \neg Q(X) \right]$$.

Each choice function on a collection X of nonempty sets is an element of the Cartesian product of the sets in X. This is not the most general situation of a Cartesian product of a family of sets, where a given set can occur more than once as a factor; however, one can focus on elements of such a product that select the same element every time a given set appears as factor, and such elements correspond to an element of the Cartesian product of all distinct sets in the family. The axiom of choice asserts the existence of such elements; it is therefore equivalent to:

 * Given any family of nonempty sets, their Cartesian product is a nonempty set.

Nomenclature
In this article and other discussions of the Axiom of Choice the following abbreviations are common:
 * AC – the Axiom of Choice. More rarely, AoC is used.
 * ZF – Zermelo–Fraenkel set theory omitting the Axiom of Choice.
 * ZFC – Zermelo–Fraenkel set theory, extended to include the Axiom of Choice.

Variants
There are many other equivalent statements of the axiom of choice. These are equivalent in the sense that, in the presence of other basic axioms of set theory, they imply the axiom of choice and are implied by it.

One variation avoids the use of choice functions by, in effect, replacing each choice function with its range:
 * Given any set X, if the empty set is not an element of X and the elements of X are disjoint, then there exists a set C such that its intersection with any of the elements of X contains exactly one element.

This can be formalized in first-order logic as:

 * ∀x (
 * ∃o (o ∈ x ∧ ¬∃n (n ∈ o)) ∨
 * ∃a ∃b ∃c (a ∈ x ∧ b ∈ x ∧ c ∈ a ∧ c ∈ b ∧ ¬(a = b)) ∨
 * ∃c ∀e (e ∈ x → ∃a (a ∈ e ∧ a ∈ c ∧ ∀b ((b ∈ e ∧ b ∈ c) → a = b))))

Note that P ∨ Q ∨ R is logically equivalent to (¬P ∧ ¬Q) → R. In English, this first-order sentence reads:

 * Given any set X,
 * X contains the empty set as an element or
 * the elements of X are not pairwise disjoint or
 * there exists a set C such that its intersection with any of the elements of X contains exactly one element.

This guarantees for any partition of a set X the existence of a subset C of X containing exactly one element from each part of the partition.

Another equivalent axiom only considers collections X that are essentially powersets of other sets:
 * For any set A, the power set of A (with the empty set removed) has a choice function.

Authors who use this formulation often speak of the choice function on A, but this is a slightly different notion of choice function. Its domain is the power set of A (with the empty set removed), and so makes sense for any set A, whereas with the definition used elsewhere in this article, the domain of a choice function on a collection of sets is that collection, and so only makes sense for sets of sets. With this alternate notion of choice function, the axiom of choice can be compactly stated as
 * Every set has a choice function.

which is equivalent to
 * For any set A there is a function f such that for any non-empty subset B of A, f(B) lies in B.

The negation of the axiom can thus be expressed as:
 * There is a set A such that for all functions f (on the set of non-empty subsets of A), there is a B such that f(B) does not lie in B.

Restriction to finite sets
The usual statement of the axiom of choice does not specify whether the collection of nonempty sets is finite or infinite, and thus implies that every finite collection of nonempty sets has a choice function. However, that particular case is a theorem of the Zermelo–Fraenkel set theory without the axiom of choice (ZF); it is easily proved by the principle of finite induction. In the even simpler case of a collection of one set, a choice function just corresponds to an element, so this instance of the axiom of choice says that every nonempty set has an element; this holds trivially. The axiom of choice can be seen as asserting the generalization of this property, already evident for finite collections, to arbitrary collections.

Usage
Until the late 19th century, the axiom of choice was often used implicitly, although it had not yet been formally stated. For example, after having established that the set X contains only non-empty sets, a mathematician might have said "let F(s) be one of the members of s for all s in X" to define a function F. In general, it is impossible to prove that F exists without the axiom of choice, but this seems to have gone unnoticed until Zermelo.

Examples
The nature of the individual nonempty sets in the collection may make it possible to avoid the axiom of choice even for certain infinite collections. For example, suppose that each member of the collection X is a nonempty subset of the natural numbers. Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set. This gives us a definite choice of an element from each set, and makes it unnecessary to add the axiom of choice to our axioms of set theory.

The difficulty appears when there is no natural choice of elements from each set. If we cannot make explicit choices, how do we know that our selection forms a legitimate set (as defined by the other ZF axioms of set theory)? For example, suppose that X is the set of all non-empty subsets of the real numbers. First we might try to proceed as if X were finite. If we try to choose an element from each set, then, because X is infinite, our choice procedure will never come to an end, and consequently we shall never be able to produce a choice function for all of X. Next we might try specifying the least element from each set. But some subsets of the real numbers do not have least elements. For example, the open interval (0,1) does not have a least element: if x is in (0,1), then so is x/2, and x/2 is always strictly smaller than x. So this attempt also fails.

Additionally, consider for instance the unit circle S, and the action on S by a group G consisting of all rational rotations, that is, rotations by angles which are rational multiples of π. Here G is countable while S is uncountable. Hence S breaks up into uncountably many orbits under G. Using the axiom of choice, we could pick a single point from each orbit, obtaining an uncountable subset X of S with the property that all of its translates by G are disjoint from X. The set of those translates partitions the circle into a countable collection of disjoint sets, which are all pairwise congruent. Since X is not measurable for any rotation-invariant countably additive finite measure on S, finding an algorithm to form a set from selecting a point in each orbit requires that one add the axiom of choice to our axioms of set theory. See non-measurable set for more details.

In classical arithmetic, the natural numbers are well-ordered: for every nonempty subset of the natural numbers, there is a unique least element under the natural ordering. In this way, one may specify a set from any given subset. One might say, "Even though the usual ordering of the real numbers does not work, it may be possible to find a different ordering of the real numbers which is a well-ordering. Then our choice function can choose the least element of every set under our unusual ordering." The problem then becomes that of constructing a well-ordering, which turns out to require the axiom of choice for its existence; every set can be well-ordered if and only if the axiom of choice holds.

Criticism and acceptance
A proof requiring the axiom of choice may establish the existence of an object without explicitly defining the object in the language of set theory. For example, while the axiom of choice implies that there is a well-ordering of the real numbers, there are models of set theory with the axiom of choice in which no individual well-ordering of the reals is definable. Similarly, although a subset of the real numbers that is not Lebesgue measurable can be proved to exist using the axiom of choice, it is consistent that no such set is definable.

The axiom of choice proves the existence of these intangibles (objects that are proved to exist, but which cannot be explicitly constructed), which may conflict with some philosophical principles. Because there is no canonical well-ordering of all sets, a construction that relies on a well-ordering may not produce a canonical result, even if a canonical result is desired (as is often the case in category theory). This has been used as an argument against the use of the axiom of choice.

Another argument against the axiom of choice is that it implies the existence of objects that may seem counterintuitive. One example is the Banach–Tarski paradox, which says that it is possible to decompose the 3-dimensional solid unit ball into finitely many pieces and, using only rotations and translations, reassemble the pieces into two solid balls each with the same volume as the original. The pieces in this decomposition, constructed using the axiom of choice, are non-measurable sets.

Moreover, paradoxical consequences of the axiom of choice for the no-signaling principle in physics have recently been pointed out.

Despite these seemingly paradoxical results, most mathematicians accept the axiom of choice as a valid principle for proving new results in mathematics. But the debate is interesting enough that it is considered notable when a theorem in ZFC (ZF plus AC) is logically equivalent (with just the ZF axioms) to the axiom of choice, and mathematicians look for results that require the axiom of choice to be false, though this type of deduction is less common than the type that requires the axiom of choice to be true.

Theorems of ZF hold true in any model of that theory, regardless of the truth or falsity of the axiom of choice in that particular model. The implications of choice below, including weaker versions of the axiom itself, are listed because they are not theorems of ZF. The Banach–Tarski paradox, for example, is neither provable nor disprovable from ZF alone: it is impossible to construct the required decomposition of the unit ball in ZF, but also impossible to prove there is no such decomposition. Such statements can be rephrased as conditional statements—for example, "If AC holds, then the decomposition in the Banach–Tarski paradox exists." Such conditional statements are provable in ZF when the original statements are provable from ZF and the axiom of choice.

In constructive mathematics
As discussed above, in the classical theory of ZFC, the axiom of choice enables nonconstructive proofs in which the existence of a type of object is proved without an explicit instance being constructed. In fact, in set theory and topos theory, Diaconescu's theorem shows that the axiom of choice implies the law of excluded middle. The principle is thus not available in constructive set theory, where non-classical logic is employed.

The situation is different when the principle is formulated in Martin-Löf type theory. There and higher-order Heyting arithmetic, the appropriate statement of the axiom of choice is (depending on approach) included as an axiom or provable as a theorem. A cause for this difference is that the axiom of choice in type theory does not have the extensionality properties that the axiom of choice in constructive set theory does. The type theoretical context is discussed further below.

Different choice principles have been thoroughly studied in the constructive contexts and the principles' status varies between different school and varieties of the constructive mathematics. Some results in constructive set theory use the axiom of countable choice or the axiom of dependent choice, which do not imply the law of the excluded middle. Errett Bishop, who is notable for developing a framework for constructive analysis, argued that an axiom of choice was constructively acceptable, saying

"A choice function exists in constructive mathematics, because a choice is implied by the very meaning of existence."

Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.

Independence
It has been known since as early as 1922 that the axiom of choice may fail in a variant of ZF with urelements, through the technique of permutation models introduced by Abraham Fraenkel and developed further by Andrzej Mostowski. The basic technique can be illustrated as follows: Let xn and yn be distinct urelements for n=1, 2, 3..., and build a model where each set is symmetric under the interchange xn ↔ yn for all but a finite number of n. Then the set X = {{x1, y{{sub|1}}}, {x2, y2}, {x3, y3}, ...} |undefined can be in the model but sets such as {{nowrap|{x{{sub|1}}, x2, x3, ...} }} cannot, and thus X cannot have a choice function.

In 1938, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model (the constructible universe) that satisfies ZFC, thus showing that ZFC is consistent if ZF itself is consistent. In 1963, Paul Cohen employed the technique of forcing, developed for this purpose, to show that, assuming ZF is consistent, the axiom of choice itself is not a theorem of ZF. He did this by constructing a much more complex model that satisfies ZF¬C (ZF with the negation of AC added as axiom) and thus showing that ZF¬C is consistent. Cohen's model is a symmetric model, which is similar to permutation models, but uses "generic" subsets of the natural numbers (justified by forcing) in place of urelements.

Together these results establish that the axiom of choice is logically independent of ZF. The assumption that ZF is consistent is harmless because adding another axiom to an already inconsistent system cannot make the situation worse. Because of independence, the decision whether to use the axiom of choice (or its negation) in a proof cannot be made by appeal to other axioms of set theory. It must be made on other grounds.

One argument in favor of using the axiom of choice is that it is convenient because it allows one to prove some simplifying propositions that otherwise could not be proved. Many theorems provable using choice are of an elegant general character: the cardinalities of any two sets are comparable, every nontrivial ring with unity has a maximal ideal, every vector space has a basis, every connected graph has a spanning tree, and every product of compact spaces is compact, among many others. Frequently, the axiom of choice allows generalizing a theorem to "larger" objects. For example, it is provable without the axiom of choice that every vector space of finite dimension has a basis, but the generalization to all vector spaces requires the axiom of choice. Likewise, a finite product of compact spaces can be proven to be compact without the axiom of choice, but the generalization to infinite products (Tychonoff's theorem) requires the axiom of choice.

The proof of the independence result also shows that a wide class of mathematical statements, including all statements that can be phrased in the language of Peano arithmetic, are provable in ZF if and only if they are provable in ZFC. Statements in this class include the statement that P = NP, the Riemann hypothesis, and many other unsolved mathematical problems. When attempting to solve problems in this class, it makes no difference whether ZF or ZFC is employed if the only question is the existence of a proof. It is possible, however, that there is a shorter proof of a theorem from ZFC than from ZF.

The axiom of choice is not the only significant statement that is independent of ZF. For example, the generalized continuum hypothesis (GCH) is not only independent of ZF, but also independent of ZFC. However, ZF plus GCH implies AC, making GCH a strictly stronger claim than AC, even though they are both independent of ZF.

Stronger axioms
The axiom of constructibility and the generalized continuum hypothesis each imply the axiom of choice and so are strictly stronger than it. In class theories such as Von Neumann–Bernays–Gödel set theory and Morse–Kelley set theory, there is an axiom called the axiom of global choice that is stronger than the axiom of choice for sets because it also applies to proper classes. The axiom of global choice follows from the axiom of limitation of size. Tarski's axiom, which is used in Tarski–Grothendieck set theory and states (in the vernacular) that every set belongs to Grothendieck universe, is stronger than the axiom of choice.

Equivalents
There are important statements that, assuming the axioms of ZF but neither AC nor ¬AC, are equivalent to the axiom of choice. The most important among them are Zorn's lemma and the well-ordering theorem. In fact, Zermelo initially introduced the axiom of choice in order to formalize his proof of the well-ordering theorem.

 * Set theory
 * Tarski's theorem about choice: For every infinite set A, there is a bijective map between the sets A and A×A.
 * Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.
 * Given two non-empty sets, one has a surjection to the other.
 * Every surjective function has a right inverse.
 * The Cartesian product of any family of nonempty sets is nonempty. In other words, every family of nonempty sets has a choice function (i.e. a function which maps each of the nonempty sets to one of its elements).
 * König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals. (The reason for the term "colloquially" is that the sum or product of a "sequence" of cardinals cannot itself be defined without some aspect of the axiom of choice.)
 * Well-ordering theorem: Every set can be well-ordered. Consequently, every cardinal has an initial ordinal.
 * Zorn's lemma: Every non-empty partially ordered set in which every chain (i.e., totally ordered subset) has an upper bound contains at least one maximal element.
 * Hausdorff maximal principle: Every partially ordered set has a maximal chain. Equivalently, in any partially ordered set, every chain can be extended to a maximal chain.
 * Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
 * Antichain principle: Every partially ordered set has a maximal antichain. Equivalently, in any partially ordered set, every antichain can be extended to a maximal antichain.
 * Abstract algebra
 * Every vector space has a basis (i.e., a linearly independent spanning subset). In other words, vector spaces are equivalent to free modules.
 * Krull's theorem: Every unital ring (other than the trivial ring) contains a maximal ideal. Equivalently, in any nontrivial unital ring, every ideal can be extended to a maximal ideal.
 * For every non-empty set S there is a binary operation defined on S that gives it a group structure. (A cancellative binary operation is enough, see group structure and the axiom of choice.)
 * Every free abelian group is projective.
 * Baer's criterion: Every divisible abelian group is injective.
 * Every set is a projective object in the category Set of sets.
 * Functional analysis
 * The closed unit ball of the dual of a normed vector space over the reals has an extreme point.
 * Point-set topology
 * The Cartesian product of any family of connected topological spaces is connected.
 * Tychonoff's theorem: The Cartesian product of any family of compact topological spaces is compact.
 * In the product topology, the closure of a product of subsets is equal to the product of the closures.
 * Mathematical logic
 * If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem; see the section "Weaker forms" below.
 * Graph theory
 * Every connected graph has a spanning tree. Equivalently, every nonempty graph has a spanning forest.

Category theory
Several results in category theory invoke the axiom of choice for their proof. These results might be weaker than, equivalent to, or stronger than the axiom of choice, depending on the strength of the technical foundations. For example, if one defines categories in terms of sets, that is, as sets of objects and morphisms (usually called a small category), or even locally small categories, whose hom-objects are sets, then there is no category of all sets, and so it is difficult for a category-theoretic formulation to apply to all sets. On the other hand, other foundational descriptions of category theory are considerably stronger, and an identical category-theoretic statement of choice may be stronger than the standard formulation, à la class theory, mentioned above.

Examples of category-theoretic statements which require choice include:
 * Every small category has a skeleton.
 * If two small categories are weakly equivalent, then they are equivalent.
 * Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint (the Freyd adjoint functor theorem).

Weaker forms
There are several weaker statements that are not equivalent to the axiom of choice but are closely related. One example is the axiom of dependent choice (DC). A still weaker example is the axiom of countable choice (ACω or CC), which states that a choice function exists for any countable set of nonempty sets. These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measurability of all sets of reals, that are disprovable from the full axiom of choice.

Given an ordinal parameter α ≥ ω+2 — for every set S with rank less than α, S is well-orderable. Given an ordinal parameter α ≥ 1 — for every set S with Hartogs number less than ωα, S is well-orderable. As the ordinal parameter is increased, these approximate the full axiom of choice more and more closely.

Other choice axioms weaker than axiom of choice include the Boolean prime ideal theorem and the axiom of uniformization. The former is equivalent in ZF to Tarski's 1930 ultrafilter lemma: every filter is a subset of some ultrafilter.

Results requiring AC (or weaker forms) but weaker than it
One of the most interesting aspects of the axiom of choice is the large number of places in mathematics where it shows up. Here are some statements that require the axiom of choice in the sense that they are not provable from ZF but are provable from ZFC (ZF plus AC). Equivalently, these statements are true in all models of ZFC but false in some models of ZF.

 * Set theory
 * The ultrafilter lemma (with ZF) can be used to prove the Axiom of choice for finite sets: Given $$I \neq \varnothing$$ and a collection $$\left(X_i\right)_{i \in I}$$ of non-empty sets, their product $$\prod_{i \in I} X_{i}$$ is not empty.
 * The union of any countable family of countable sets is countable (this requires countable choice but not the full axiom of choice).
 * If the set A is infinite, then there exists an injection from the natural numbers N to A (see Dedekind infinite).
 * Eight definitions of a finite set are equivalent.
 * Every infinite game $$G_S$$ in which $$S$$ is a Borel subset of Baire space is determined.
 * Measure theory
 * The Vitali theorem on the existence of non-measurable sets, which states that there exists a subset of the real numbers that is not Lebesgue measurable.
 * There exist Lebesgue-measurable subsets of the real numbers that are not Borel sets. That is, the Borel σ-algebra on the real numbers (which is generated by all real intervals) is distinct from the Lebesgue-measure σ-algebra on the real numbers.
 * The Hausdorff paradox.
 * The Banach–Tarski paradox.
 * Algebra
 * Every field has an algebraic closure.
 * Every field extension has a transcendence basis.
 * Every infinite-dimensional vector space contains an infinite linearly independent subset (this requires dependent choice, but not the full axiom of choice).
 * Stone's representation theorem for Boolean algebras needs the Boolean prime ideal theorem.
 * The Nielsen–Schreier theorem, that every subgroup of a free group is free.
 * The additive groups of R and C are isomorphic.
 * Functional analysis
 * The Hahn–Banach theorem in functional analysis, allowing the extension of linear functionals.
 * The theorem that every Hilbert space has an orthonormal basis.
 * The Banach–Alaoglu theorem about compactness of sets of functionals.
 * The Baire category theorem about complete metric spaces, and its consequences, such as the open mapping theorem and the closed graph theorem.
 * On every infinite-dimensional topological vector space there is a discontinuous linear map.
 * General topology
 * A uniform space is compact if and only if it is complete and totally bounded.
 * Every Tychonoff space has a Stone–Čech compactification.
 * Mathematical logic
 * Gödel's completeness theorem for first-order logic: every consistent set of first-order sentences has a completion. That is, every consistent set of first-order sentences can be extended to a maximal consistent set.
 * The compactness theorem: If $$\Sigma$$ is a set of first-order (or alternatively, zero-order) sentences such that every finite subset of $$\Sigma$$ has a model, then $$\Sigma$$ has a model.

Possibly equivalent implications of AC
There are several historically important set-theoretic statements implied by AC whose equivalence to AC is open. Zermelo cited the partition principle, which was formulated before AC itself, as a justification for believing AC. In 1906, Russell declared PP to be equivalent, but whether the partition principle implies AC is the oldest open problem in set theory, and the equivalences of the other statements are similarly hard old open problems. In every known model of ZF where choice fails, these statements fail too, but it is unknown whether they can hold without choice.

 * Set theory
 * Partition principle: if there is a surjection from A to B, there is an injection from B to A. Equivalently, every partition P of a set S is less than or equal to S in size.
 * Converse Schröder–Bernstein theorem: if two sets have surjections to each other, they are equinumerous.
 * Weak partition principle: if there is a injection and a surjection from A to B, then A and B are equinumerous. Equivalently, a partition of a set S cannot be strictly larger than S. If WPP holds, this already implies the existence of a non-measurable set. Each of the previous three statements is implied by the preceding one, but it is unknown if any of these implications can be reversed.
 * There is no infinite decreasing sequence of cardinals. The equivalence was conjectured by Schoenflies in 1905.
 * Abstract algebra
 * Hahn embedding theorem: Every ordered abelian group G order-embeds as a subgroup of the additive group $$\mathbb{R}^\Omega$$ endowed with a lexicographical order, where Ω is the set of Archimedean equivalence classes of G. This equivalence was conjectured by Hahn in 1907.

Stronger forms of the negation of AC
If we abbreviate by BP the claim that every set of real numbers has the property of Baire, then BP is stronger than ¬AC, which asserts the nonexistence of any choice function on perhaps only a single set of nonempty sets. Strengthened negations may be compatible with weakened forms of AC. For example, ZF + DC + BP is consistent, if ZF is.

It is also consistent with ZF + DC that every set of reals is Lebesgue measurable, but this consistency result, due to Robert M. Solovay, cannot be proved in ZFC itself, but requires a mild large cardinal assumption (the existence of an inaccessible cardinal). The much stronger axiom of determinacy, or AD, implies that every set of reals is Lebesgue measurable, has the property of Baire, and has the perfect set property (all three of these results are refuted by AC itself). ZF + DC + AD is consistent provided that a sufficiently strong large cardinal axiom is consistent (the existence of infinitely many Woodin cardinals).

Quine's system of axiomatic set theory, New Foundations (NF), takes its name from the title ("New Foundations for Mathematical Logic") of the 1937 article that introduced it. In the NF axiomatic system, the axiom of choice can be disproved.

Statements implying the negation of AC
There are models of Zermelo-Fraenkel set theory in which the axiom of choice is false. We shall abbreviate "Zermelo-Fraenkel set theory plus the negation of the axiom of choice" by ZF¬C. For certain models of ZF¬C, it is possible to validate the negation of some standard ZFC theorems. As any model of ZF¬C is also a model of ZF, it is the case that for each of the following statements, there exists a model of ZF in which that statement is true.

 * The negation of the weak partition principle: There is a set that can be partitioned into strictly more equivalence classes than the original set has elements, and a function whose domain is strictly smaller than its range. In fact, this is the case in all known models.
 * There is a function f from the real numbers to the real numbers such that f is not continuous at a, but f is sequentially continuous at a, i.e., for any sequence {xn} converging to a, limn f(xn)=f(a).
 * There is an infinite set of real numbers without a countably infinite subset.
 * The real numbers are a countable union of countable sets. This does not imply that the real numbers are countable: As pointed out above, to show that a countable union of countable sets is itself countable requires the Axiom of countable choice.
 * There is a field with no algebraic closure.
 * In all models of ZF¬C there is a vector space with no basis.
 * There is a vector space with two bases of different cardinalities.
 * There is a free complete Boolean algebra on countably many generators.
 * There is a set that cannot be linearly ordered.
 * There exists a model of ZF¬C in which every set in Rn is measurable. Thus it is possible to exclude counterintuitive results like the Banach–Tarski paradox which are provable in ZFC.  Furthermore, this is possible whilst assuming the Axiom of dependent choice, which is weaker than AC but sufficient to develop most of real analysis.
 * In all models of ZF¬C, the generalized continuum hypothesis does not hold.

For proofs, see.

Additionally, by imposing definability conditions on sets (in the sense of descriptive set theory) one can often prove restricted versions of the axiom of choice from axioms incompatible with general choice. This appears, for example, in the Moschovakis coding lemma.

Axiom of choice in type theory
In type theory, a different kind of statement is known as the axiom of choice. This form begins with two types, σ and τ, and a relation R between objects of type σ and objects of type τ. The axiom of choice states that if for each x of type σ there exists a y of type τ such that R(x,y), then there is a function f from objects of type σ to objects of type τ such that R(x,f(x)) holds for all x of type σ:

(\forall x^\sigma)(\exists y^\tau) R(x,y) \to (\exists f^{\sigma \to \tau})(\forall x^\sigma) R(x,f(x)). $$ Unlike in set theory, the axiom of choice in type theory is typically stated as an axiom scheme, in which R varies over all formulas or over all formulas of a particular logical form.

title: Axiom of choice