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Talk:Axiom of determinacy

Infinite logic
I just dropped a passage on infinite logic and the axiom of determinacy. The particular version of infinite logic in which this can be done I'm not sure of. One exists obviously but it may be inconsistent. This is just because the axiom of determinacy may be inconsistent. Barnaby dawson 17:54, 24 Oct 2004 (UTC)

 * Cool, thanks for your additions! -- Schnee 20:34, 24 Oct 2004 (UTC)

Independence of independence from ZF
The article says:

 * It is also conceivable that the independence of AD is independent (i.e in some models of ZF you can resolve AD and in some you cannot).

Is that actually possible? -- Schnee 15:46, 31 Oct 2004 (UTC)

Yes it's possible that a model of ZF has non-standard integers that code for proofs that can't be expressed as normal integers. So a proof of AD's consistancy may require a non-standard integer and so depend on the model of ZF we're in (This would make the independence of AD independent). I don't think that current thinking rules this out as a possibility. It's weird isn't it :) Barnaby dawson 21:14, 31 Oct 2004 (UTC)

 * Yeah, and I'm not sure I understand that actually (which may be due to the fact that I'm an undergraduate who's only heard a few lectures about axiomatic set theory and the like - despite having an interest in these things, I'm really just a mathematical layman). I mean... if you consider all models of ZF (assuming that there are any at all ^_~), then you can divide them into two classes - those in which AD holds and those in which it doesn't. If one of those classes is empty, then by Gödel's completeness theorem, it follows that ZF implies AD or -AD (depending on which of them is empty). If neither is, then AD is independent of ZF. Or am I making a mistake here somewhere?

The axiom of choice vs. axiom of determinacy needs work. 1st of all, the proof is a variation of Cantor  and should be mentioned as such. 2nd of all, many determinancies  are not infinite -  therefore an infinite game cannot be used to prove the difference between AC and AD. 146.115.82.167 (talk) 14:01, 4 May 2017 (UTC)
 * And also, different models of ZF with integers that fundamentally differ from those in other models shouldn't play a role here really; as long as the rules of deduction that you use for proofs (and that actually define just what formal proving is) don't change, what can and cannot be proven shouldn't change.

 * -- Schnee 21:56, 31 Oct 2004 (UTC)

The text contains: "The axiom of determinacy is independent of ZF (assuming that ZF is consistent); it does not follow from ZF (since AC is independent of ZF), but it is possible to construct models of ZF where AD holds (cf. Jech, Set theory)."

Two of these statements are false. Assuming consistency of ZF the axiom of determinacy cannot be proved to be independent of ZF (in ZF). This is because ZF+AD is eqiconsistent with ZF+"There exist infinitely many woodin cardinals". This implies the consistency of ZF. If ZF implied consistency of ZF+"infinitely many woodin cardinals" then ZF+"There exist infinitely many woodin cardinals" would imply its own consistency and would therefore be inconsistent. It is not possible to construct models of ZF where AD holds without futher large cardinal axioms. In fact (Jech, set theory) makes this point. As such I'm correcting the text. Barnaby dawson 12:26, 7 Nov 2004 (UTC)

 * OK, thanks. I don't actually had the Jech book for a reference myself; I was merely given this information by someone else. Goes to show you should only trust those claims you made up yourself, I guess. ;) -- Schnee 13:01, 7 Nov 2004 (UTC)

The article no longer uses the term 'independence' at all. I just did a search of the article for 'indep' and it was not found. What it does say is "AD implies the consistency of ZF. Hence it is not possible to prove AD in ZF (a consequence of the incompleteness theorems)." (i.e., AD is independent). Since we can prove the independence of AD (assuming ZF is consistent), the independence of AD cannot itself be independent! If it were, there would be models of ZF in which AD is not independent, i.e., in which AD can be proven from ZF, which contradicts the fact that it is provably impossible to prove AD, so it cannot be proven in any model of ZF.

This means the class of models in which AD is false cannot be empty. In fact, in 1930 Gödel proved that if ZF is consistent, so is ZFC, i.e. there are models in which AC is true. In all such models AD is false, since AD is incompatible with AC.--Hccrle (talk) 09:23, 26 April 2008 (UTC)

Notes on needed improvements
(mostly notes to myself, but everyone can see what I'm thinking and argue with me/do it first).

 * It is possible that the axiom of determinacy can be proved false without the use of the axiom of choice.

The above is true in some formal sense; not a serious possibility. It's also true in some formal sense that it's possible PA can prove 0=1.

 * It's not the same at all. It is quite possible that the Axiom of determinacy is false.  And postulating the consistency of the axiom of determinacy it isn't at all like postulating the consistency of PA.  We can't get the consistency of the axiom of determinacy without postulating very large cardinals which are also suspect.  Barnaby dawson 14:40, 11 July 2005 (UTC)

 * What is PA? To say it's possible PA can prove 0=1 is to say it's possible to prove PA is false, but what is it? Nowhere on this page or in the article is the term "PA" defined. Do you mean Peano's Arithmetic? Surely you jest. --Hccrle (talk) 10:06, 26 April 2008 (UTC)

 * The large cardinals are not really that suspect, these days. AD is of course definitely false, not just possibly, because AC is true, but it's not a significant possibility that AD is inconsistent with ZF.--Trovatore 16:03, 11 July 2005 (UTC)

 * We might state that this is the view of most mathematicians working in set theory but the quoted sentence should remain. Barnaby dawson 17:18, 11 July 2005 (UTC)
 * Perhaps neutral language would say something like "It is not possible to prove in ZF that ZF is consistent with AD", without comment on whether this outcome is philosophically "possible" --Trovatore 17:33, 11 July 2005 (UTC)

 * Yup. Done. Barnaby dawson 21:01, 11 July 2005 (UTC)

Need section on consequences of AD. The blurb about AD implying measurability and p.o.B for sets of reals is not prominent enough, and lots of things are left out.

Need section on fragments of AD that follow from large cardinals.
 * This will now be in Determinacy; no need to duplicate it here.

--Trovatore 17:16, 3 September 2005 (UTC)

Proof that AC==>~AD -- maybe move to WikiProofs?

 * Again I disagree. It might be better to put a more intuitive proof.  But this proof is pretty vital to the article.  AD is non standard (although important) and that should be clear.  Barnaby dawson 14:40, 11 July 2005 (UTC)

 * Well, it's just a bit long. The fact that AD is inconsistent with AC follows directly from the facts mentioned elsewhere about AD implying regularity properties for sets of reals.  That would leave more room to (i) define games better, (ii) say more about where AD fits in the scheme of things, and (iii) more about its consequences, without making the article too long and unfocused.--Trovatore 16:03, 11 July 2005 (UTC)
 * Update: (i), (ii), and some of (iii), will now be handled in Determinacy.  For thoughts on aspects of (iii) that should still be handled in Axiom of determinacy, see  below. --Trovatore 17:16, 3 September 2005 (UTC)

 * I think an elementary proof is much more appropriate on wikipedia. I know one involving an intuitive and simple game.  I may work on that later this week.  Barnaby dawson 17:18, 11 July 2005 (UTC)

 * I think we can afford to make this article significantly longer without any trouble. I agree with points (i), (ii) and (iii) although sadly I don't yet know enough to help out much (I could help out with (i)).

 * By the way I can't seem to find this wikiproofs that you speak of. Doesn't turn up on google.  I can find the meta discussion page concerning it though.  Looks like a great idea I should add.  Barnaby dawson 21:01, 11 July 2005 (UTC)

Definition of AD is not entirely clear -- an example of a "two-player game of perfect information of length $$\omega$$" should be given.
 * Update: See Determinacy for this. Perhaps not necessary to duplicate that content in this article. --Trovatore 17:16, 3 September 2005 (UTC)

References are a bit quirky; Jech is the only standard ref. Give some others. --Trovatore 07:09, 11 July 2005 (UTC)
 * Update: this is better now. --Trovatore 17:16, 3 September 2005 (UTC)

New Determinacy article
I've written (well, started) a new Determinacy article, intended to be the central reference point for the new Category:Determinacy, that treats determinacy in a more general context than just the axiom of determinacy. It is not intended to supplant this article, but to complement it. However it's possible that there's some content in Axiom of determinacy that really belongs in Determinacy, now that it exists -- I'll think about this later. Maybe. --Trovatore 05:15, 2 September 2005 (UTC)
 * Actually, I don't think any content needs to be moved out of Axiom of determinacy. The "types of games that are determined" content will probably be redundantly treated in Determinacy, but it's short and has expository value, so it's OK where it is.  Mainly there's content that I thought needed to be added to Axiom of determinacy, that now ought to go in Determinacy instead. --Trovatore 05:19, 2 September 2005 (UTC)

Additions still needed to this article
A list of a few things that come to mind that still need to be added, and belong in this article, not in the little Axiom of determinacy subsection of the Determinacy article. (That subsection isn't written yet, but is expected to say what AD is, that it is provably false from ZFC, that it's true in L(R) (assuming large cardinals), and then point to this article for more detailed information). --Trovatore 16:45, 3 September 2005 (UTC)
 * 1) Consequences of AD for the alephs (e.g. ℵ1 and ℵ2 are measurable, ℵn for finite n≥3 are all singular with cofinality ℵ2.
 * 2) Nonexistence of an uncountable wellordered sequence of distinct reals, or even distinct countable sets of reals.
 * 3) The coding lemma (should probably have its own article, but there should be a blurb here).
 * 4) The projective ordinals, such as δ13 (idem).
 * 5) Models of AD, beyond L(R).

Template:Technical
Okay, I don't understand this article. At all. In fact, I don't think I understand a single sentence beyond the first. Of course, I'm a layman, so I can't expect to understand it fully without some set theory courses (unless it's a bit more basic than I think), but I could at least have some idea of a) what it implies for easily-understandable concepts, b) what direct or indirect practical applications it may have, and c) how important it is in its field, probably in addition to at least some other stuff. Surely this concept is no more advanced than, say, quantum chromodynamics (at least the latter has a much fancier name ;)), but the latter has an introduction that's mostly understandable to high-school graduates. —Simetrical (talk) 03:25, 26 December 2005 (UTC)

 * You must have gone to an unusual high school, but yes, I agree that this article could use a better intro (and not just from an accessibility point of view). Take a look at Determinacy and see if that helps any, and if there's anything from there you think might be imported to this article. --Trovatore 21:42, 28 December 2005 (UTC)

 * I also found the article very confusing until I had a look at that link. What I'm going to do is change the link on the word "games" in the third sentence (the statement of the axiom itself) to point to that link instead of to "game theory". After all, what that link does is explain what sort of game this axiom is talking about, and that was just the missink link I needed to understand it. 91.105.63.245 (talk) 19:57, 20 April 2008 (UTC)
 * Actually I don't agree with the link to game theory. Game theory is almost exclusively about games of imperfect information -- games of perfect information (at least, with only two players) are considered kind of trivial from a game-theoretic perspective. They may not be trivial in practice, of course, but the parts of them that are difficult are not interesting to game theorists qua game theorists. I can believe that the link to a section of determinacy may not have been ideal, but I think it's better than a link to game theory. --Trovatore (talk) 21:31, 20 April 2008 (UTC)
 * Whoops, now I see that we're in "violent agreement". Sorry about that -- I read the diffs backwards. --Trovatore (talk) 21:55, 20 April 2008 (UTC)

Choice
Is there something known about what weaker forms of AC are consistent with AD? I would really like to see wether DC or something even stronger is compatible with AD or not, or is it undecidable that it is undecidable to decide? XD Scineram 15:48, 1 September 2006 (UTC)

Yes, Kechris proved that: if AD holds, then AD+DC holds in L(R). It is not easy. Kope 16:27, 1 September 2006 (UTC)

Why AC contradicts the AD
In the point 2 of that paragraph it is stated: "The set of possible outcomes of this strategy which we have already decided on has cardinality less than the continuum. (By choice of well ordering and the fact that we only decide on one outcome per strategy)"

If the outcome of the strategy considered actually depends upon what the other player does at infinitely many points in the game, then I understand that the cardinality of possible outcomes of the strategy considered will be equal to continuum. Correct me if I am wrong. -- Leocat 17:55, 29 October 2006 (UTC)
 * No, you're right. But the proof is also right, just a bit unclearly written, I think. The set asserted to have cardinality less than c is "the set of possible outcomes of this strategy which we have already decided on". Here to "decide on" an outcome means to decide which player wins that outcome.
 * The language of the proof clearly needs a cleanup. Once you've followed the proof, maybe you'd volunteer to clean it up; you would know what parts of it were unclear to you on a first reading, which should give you a leg up. --Trovatore 19:26, 29 October 2006 (UTC)

I still see the cardinality of possible outcomes of the strategy that we have decided on as continuum, if the outcome depends upon what the other player does at infinitely many points in the game. -- Leocat 21:26, 29 October 2006 (UTC)
 * You're getting hung up on "possible outcomes" whereas you should be focusing on "what we have decided". We're taking the strategies one at a time, in order type c. So for example if c is $$\aleph_{17}$$, then at any given stage of the iteration, we have thus far made only (at most) $$\aleph_{16}$$ decisions, and each of these decisions assigns the winner for only one outcome. But there are, as you correctly observe, $$\aleph_{17}$$ possible outcomes consistent with the strategy we're currently considering. That's how we know there's an outcome (consistent with the strategy being considered) to which we haven't currently assigned a winner. We assign a winner in such a way that the strategy being considered loses, and move on.
 * When we get to the end, we've refuted all possible strategies. Therefore there is no winning strategy for the game, for either player, and thus AD is false. --Trovatore 06:03, 30 October 2006 (UTC)

 * Let the players be Alice and Bob. For each of Alice's strategies, we choose a sequence of moves by Bob which leads to an outcome (one of the continuum many) which has not yet been decided. Then we decide that in favor of Bob. Consequently, that strategy of Alice's will not be a winning strategy. Similarly, for each of Bob's strategies, we pick a sequence of moves for Alice which lead to an as yet undetermined outcome. We decide that outcome in favor of Alice. Thus Bob's strategy is not a winning strategy. Since neither player has a winning strategy, the game is not determined. Got it? JRSpriggs 08:28, 30 October 2006 (UTC)

A set A of sequences is determined if there exists an absolutely winning strategy for one of the players, say for Alice. The question is not what happens when Alice does not follow the winning strategy. If she does, then you cannot choose a sequence of moves by Bob to make him win. -- Leocat 19:59, 31 October 2006 (UTC)

 * Not sure I take your point. The idea of the proof is to construct such a set A, for which there is no winning strategy. This is done by making sure that, for any strategy Alice might try, there's a play by Bob that defeats it, and mutatis mutandis. --Trovatore 20:17, 31 October 2006 (UTC)

 * To Leocat: You seem to be assuming that we are given a fixed game. On the contrary, to disprove the axiom of determinacy, we are using the axiom of choice to help us "construct" a game which is not determined. The only difficulty in the construction is the possibility that, when trying to defeat Alice's strategies, we might run out of sequences of moves for Bob; or, when trying to defeat Bob's strategies, we might run out of sequences of moves for Alice. We can use the axiom of choice to order the strategies and outcomes in a way that allows us to avoid running out. JRSpriggs 10:18, 1 November 2006 (UTC)

part 2
To JRSpriggs: You "refute" each strategy, but this refutation is only conditional - you have to specify countably many further conditions to make Alice win or lose. When all of these conditions are specified, it may turn out that one of the "refuted" strategies is a winning strategy. -- Leocat 10:31, 1 November 2006 (UTC)

 * See Determinacy. You do not appear to understand what is meant by "strategy". A strategy for Alice is a function from the set of all possible finite sequences of moves by Bob to Alice's next move following the last move in that sequence. So given a strategy for Alice and an ω-sequence of moves by Bob, we get the entire play of the game, i.e. all the moves of Alice and Bob. There is nothing left to do, but decide who won. There are no "further conditions" to specify. JRSpriggs 11:47, 1 November 2006 (UTC)

I have no problem with the concept of strategy. The statement: "If you give me a strategy S then we considered that strategy at some time t = t(S)" is the source of misunderstanding. It should be stated that the "time axis" here is the long line whose length is continuum. -- Leocat 18:57, 1 November 2006 (UTC)

 * There are two different notions of time here, which may be causing confusion. One notion is the time in the play of the game: Alice's first move, Bob's first move, Alice's second move, Bob's second move, etc.. This time may be indexed by natural numbers. The other notion of time is a stage in the construction of the game: deciding an outcome to refute Alice's first strategy, deciding an outcome to defeat Bob's first strategy, deciding an outcome to refute Alice's second strategy, etc.. This time may be indexed by ordinals less than the initial ordinal of the continuum. The sentence you quoted refers to this second notion of time. JRSpriggs 07:41, 2 November 2006 (UTC)

I claim that the AD is simply false and can be disproved without AC, so it does not matter that you can construct a proof that uses AC. Let Bob have an almost-winning strategy SB0 which simply produces the sequence of zeros. Let it win against every Alice's strategy except SA0 which can consist in producing a sequence containing all prime numbers. Let SA0 lose against SB1 (which can be producing a sequence containing all powers of 2) and let SB1 lose in all other cases. This simple procedure defines a game that is not determined. -- Leocat 17:55, 3 November 2006 (UTC)
 * I'm not sure what the game is, that you claim to have defined. What we know is that

ALICE a0  a1  a2  a3  ... BOB       0   0   0   0 ...

 * is a win for Bob, no matter what a0, a1, a2... are, except for the single case

ALICE 2   3   5   7  ... BOB      0   0   0   0 ...

 * which is a win for Alice. Also we know that

ALICE 2    3   5    7  ... BOB      1    2   4    8 ...

 * is a win for Bob. But to know what the game is we need to know who wins an arbitrary outcome, and you haven't told us who wins anything that doesn't fit into one of the above three cases. --Trovatore 18:21, 3 November 2006 (UTC)

 * Oh, I guess you have given one further piece of information, which is that

ALICE a0    a1   a2    a3  ... BOB       1     2    4    8 ...
 * is always a win for Alice, except in the third case above. We're still not close to defining a game. --Trovatore 18:23, 3 November 2006 (UTC)

You are right. I will take another look at the proof. -- Leocat 18:56, 3 November 2006 (UTC)

I think you should consider all pairs of strategies and make sure that for every strategy there is one that wins against it. This is not very clear from the presented proof. Also, the statement in point 2 about cardinality is false in all cases of strategies that actually depend upon what the other player does at infinitely many points. -- Leocat 19:28, 3 November 2006 (UTC)

Leocat's latest changes
Hi Leocat,

I appreciate that you're trying to improve the proof, which has been in need of it for quite some time. But your latest changes are problematic as they stand.
 * First of all, there's no need to iterate through pairs of strategies. Given a strategy for (say) Alice, all you need to find is one play by Bob that beats it. There's no need to consider all of Bob's possible strategies.
 * Also, it's not clear what you mean by
 * 3. Decide that this sequence belongs to A, i.e. s1(T) won against s2(T).

 * The problem is that you may already have decided that the sequence is not in A. That's because the same sequence may have been generated by two different strategies, already considered earlier.
 * Finally, I think the "two notions of time" thing is confusing. I would just avoid talking about "time" entirely. To the extent that I do think of it in terms of "time", I would consider the individual plays of the game to be instantaneous—we aren't really considering anything happening sequentially within an individual game. --Trovatore 06:52, 7 November 2006 (UTC)

1) There is a need to consider all of Bob's strategies, because we have to make sure that every Bob's strategy will lose against a properly chosen strategy of Alice and vice versa. 2) I think you are right that a given sequence may have been already generated by a different pair of strategies and then it would have been already decided whether it belongs to A or not. I do not see a solution of this problem at the moment. -- Leocat 18:43, 7 November 2006 (UTC)
 * Yes, you do have to consider every strategy of Bob's. But you don't have to consider all pairs of strategies for Alice and strategies for Bob. It's enough to alternate between strategies for Alice and strategies for Bob, making sure you refute each such individual strategy. Pairs of strategies never come up.
 * The proof you modified had a correct solution to this, though it was admittedly not very clearly worded. I think you should go back and look at it and figure out what it was saying. --Trovatore 18:57, 7 November 2006 (UTC)

What are closed sets or Borel sets of INTEGERS? -- Leocat 16:26, 8 November 2006 (UTC)
 * Answering the question literally -- the integers are usually given the discrete topology, so every set of integers is closed and Borel.
 * Trying to read your mind a bit -- when we speak of games whose payoff set is closed, or Borel, we're not talking about sets of integers, but rather sets of sequences of integers. These are given the product topology. A basic open set is defined by specifying finitely much of the sequence, and taking all possible extensions.

Now to the more serious matter: Your proof is still not correct (though it's an improvement over your previous effort). Your second step
 * 2. Go through the entire game, generating a sequence {a(1),a(2),...,a(t),...}.

cannot be carried out, because we don't know what the second player played. You can remedy that by specifying what the second player played, but you need to make sure that the sequence that results is not one for which you've already made an A-or-not-A decision. The cardinality argument of the original proof, or something fulfilling the same function, is going to be needed. --Trovatore 21:50, 8 November 2006 (UTC)

I guess my choice of symbols did not make it clear what I meant - so I changed it to make it clear that we are talking about sequences generated by our procedure together with the currently considered strategy. -- Leocat 10:55, 10 November 2006 (UTC)
 * So step 2 is not as clear as it could be, but much worse is step 7:
 * Keep repeating with further strategies if there are any, making sure that sequences already considered do not become generated again.
 * How do you propose to "make sure" of that? --Trovatore 05:09, 11 November 2006 (UTC)

You can start with the set of all sequences and keep choosing elements from it without returning them. If you choose an element {a(1),a(2),a(3),...,a(n),...} you will use it e.g. to make the sequence {c(1),d(2),c(3),d(4),...} by assigning c(1)=a(1),c(3)=a(2),...,c(2n-1)=a(n),... . -- Leocat 16:04, 11 November 2006 (UTC)
 * I take it this is when refuting a strategy for the second player, correct? But how do you know that you haven't used the sequence {a(1),a(2),a(3),...} already? --Trovatore 20:26, 11 November 2006 (UTC)

Let G be the set of all sequences of natural numbers. We start from this set and every time we choose a sequence we obtain a smaller set, which does not contain any of the sequences that have already been chosen. But this still does not solve the problem. -- Leocat 15:50, 12 November 2006 (UTC)
 * You're right, it doesn't. The point is, how do you know you don't exhaust G, before you get to the end of the construction? There is a way to handle this; it was there in the original proof. --Trovatore 20:28, 12 November 2006 (UTC)

There always exists a bijection between sets of the same cardinality, so I do not think it is a problem that you exhaust G before you get to the end of the construction. The problem is to keep constructing sequences and making decisions regarding their membership in A without contradicting yourself. I believe it can be done. I do not see the solution of this problem in the original proof. Also, the cardinality argument in step 2 of the original proof is false, as I already pointed out. -- Leocat 18:09, 15 November 2006 (UTC)

 * No, it was correct; you didn't understand it. Not entirely your fault, as it wasn't clearly written. But it's a key point, and you won't have a correct proof until you do understand it. How do you know you don't exhaust G by the end of the construction? Hint: At any given point in the construction, what do you know about the part of G that has been used? --Trovatore 18:33, 15 November 2006 (UTC)

At any given point in the construction we know that the cardinality of the part of G that has been used is less than continuum. But I do not see how it helps in making sure that we dot generate any sequence more than once. -- Leocat 14:54, 20 November 2006 (UTC)

 * How big is G? --Trovatore 18:11, 20 November 2006 (UTC)

 * At any stage in the construction of the game G, there are continuum many outcomes (sequences of moves for both Alice and Bob), but the subset of them which have been designated as wins for Alice or wins for Bob is less than the continuum. If we project this onto the sequence of Bob's moves (in the process of refuting Alice's strategies), we see that there are continuum many sequences of moves for Bob, but the subset which have been used is less than continuum many. So we are free to choose a sequence for Bob which has not yet been used; and use it to refute Alice's current strategy. Since the moves for Bob are different than any already designated, the entire outcome (both Alice's moves and Bob's moves) must be different. Similarly when choosing sequences of moves for Alice to refute Bob's current strategy. At the end, any outcomes not yet designated may arbitrarily be designated as wins for (say) Alice. Then all strategies of either player have been refuted and the game is not determined.

 * If we did not know that the number of outcomes already designated was less than the continuum, we could not be sure that we could choose a sequence of moves for Bob with which to refute Alice's current strategy. So we could not be sure that it was not a winning strategy for Alice. So the game might be determined. JRSpriggs 08:28, 21 November 2006 (UTC)

Things are a little bit more difficult: just because we choose a different sequence of Bob's moves each time we refute Alice's strategy does not guarantee that we do not generate a sequence more than once, because a given sequence of Bob's moves could have been already generated when refuting a Bob's strategy. But there is a simple solution to this problem: each time we refute a strategy, we take projections of the generated sequence onto Bob's moves and onto Alice's moves and we take away both of these sequences from the set of sequences that have not been used yet. -- Leocat 10:20, 21 November 2006 (UTC)

 * You are misinterpreting what I said. I meant that ALL outcomes whether from refuting Alice or refuting Bob would be projected before each selection of a new sequence to refute one of their strategies. So your "correction" is already incorporated in my answer. JRSpriggs 11:20, 21 November 2006 (UTC)

On Types of Games That Are Determined
The article says:

 * It follows from the existence of sufficient large cardinals that ... and that AD holds in L(R).

How can this be when, in L(R), L(R)=L=V. Therefore in such models AC holds, so AD cannot also hold? --Hccrle (talk) 09:47, 26 April 2008 (UTC)
 * You have a false premise -- it's not true that L(R) satisfies V=L. For example L(R) contains 0#, and is able to see that 0# is not an element of L (but that it is an element of L(R)). --Trovatore (talk) 21:23, 26 April 2008 (UTC)

continuum hypothesis
It's probably worth talking about the CH issue a little on the discussion page, because it's not entirely simple.

For the purposes of this discussion (not for the article of course!) let's agree to use the term "weak CH" for the proposition every set of reals is either countable or equinumerous with the reals, and "strong CH" for $$2^{\aleph_0}=\aleph_1$$. This terminology passes at least the minimal sanity check that, over ZF, strong CH implies weak CH, but not vice versa. Over ZFC, the two propositions are equivalent.

Then over ZF, AD implies weak CH but is actually inconsistent with strong CH.

Normally in the literature no distinction is made between the two. But that's because the axiom of choice is part of the background in the default context. That's also true for the informal set theory of Cantor in the context in which CH was originally proposed (Cantor did not know of AC in its modern form, but proposed as "a law of thought" that every set can be wellordered).

So there doesn't seem to be any completely canonical choice for which of these (if either) should be called "the continuum hypothesis" in a context where AC fails. However I would argue that strong CH is the more natural one to call "the continuum hypothesis" from the point of view of a contemporary set theorist. Two examples of why: Hope this explains my edits to the lede. --Trovatore (talk) 21:00, 23 April 2009 (UTC)
 * It's a natural thing to start with a model of, say, ZF+AD+V=L(R), and "force CH to be true" by adding a generic bijection between R and $$\aleph_1$$; the extension is then a model of ZFC.
 * Strong CH has a simpler logical form than weak CH — this is maybe surprising on the face of it, because strong CH is harder for beginners to parse, but it's true. Strong CH says "there is a wellordering of R whose every proper initial segment is countable".  That can be coded as saying that there exists a set of reals with a certain property, where to define the property you need quantify only over reals, so it's $$\Sigma^2_1$$.  Weak CH on the other hand says that for every set of reals, if it's uncountable, then there is some bijection of it with R; that is, that there is some set of reals coding the bijection.  So it's $$\Pi^2_2$$, strictly more complicated.

 * This is not the place to discuss what continuum hypothesis is. Our article continuum hypothesis defines it as the "weak CH" (or actually, as "there is no cardinality strictly between $$\aleph_0$$ and $$2^{\aleph_0}$$" which is even weaker, it does not imply that every cardinality below continuum is comparable with $$\aleph_0$$). If you think this is inappropriate, you should raise it on Talk:Continuum hypothesis, not here. I find it quite silly and confusing to talk about a "weak form of CH" when it is actually stronger than what the reader finds after clicking the link to continuum hypothesis.

 * Whatever the definition of CH is, I tried to clarify the issue by formulating exactly what the AD implies in the sentence, but you removed it, I wonder what was the rationale for that. — Emil J. 10:05, 24 April 2009 (UTC)
 * Wikipedia articles stand on their own. It's irrelevant what the linked article says.
 * (or, maybe more important — of course, the linked continuum hypothesis article is talking in the default set-theoretic context, which includes the axiom of choice. That means that the definition given there is fine, there.  But in this article we necessarily step outside of that context.)
 * However the point about the inline explanation is well-taken. --Trovatore (talk) 18:01, 24 April 2009 (UTC)

Measurablility?
The article currently states:
 * the axiom of determinacy implies that all subsets of the real numbers are Lebesgue measurable

This begs the question: what about the Banach-Tarski paradox? what about the Vitali sets? I guess that the statement "incompatible with CH" takes care of these, but a more explicit development would be nice. linas (talk) 16:30, 8 May 2010 (UTC)
 * Because AD implies that all sets of reals are measurable, it immediately follows that it refutes Banach-Tarski and the existence of the Vitali set. I suppose that would be worth mentioning.  (Note that just because AD is incompatible with AC does not in itself imply that AD refutes Banach-Tarski or the Vitali set.) --Trovatore (talk) 17:26, 8 May 2010 (UTC)
 * Hmm, actually, on rethinking it, I suppose I don't see an immediate argument from the measurability of all subsets of R to the measurability of all subsets of R3, which is what you need to directly refute Banach-Tarski. But AD certainly proves the measurability of all subsets of R3, and the argument is going to be essentially identical to the proof for subsets of R.  --Trovatore (talk) 18:37, 8 May 2010 (UTC)

Herrlich has this quote in his book (ISBN 3540309896), in the section on AD: If a model of ZF satisfies AD, then this model is closer to physical reality than any model of ZFC. For example, the Banach–Tarski paradoxical decomposition of a ball is impossible. V.W. Marek and J. Mycielski

The paper cited is V.W. Marek and J. Mycielski. Foundations of mathematics in the twentieth century. Amer. Math. Monthly, 108:449–468, 2001

Help requested at extensive-form games
By the way, can someone (meaning Trovatore almost surely) look at the infinite action spaces section of Extensive-form game (the game described here is of that kind). Herrlich says that omega-long games and games where the action sets have omega cardinality are "complementary", but I'm not sure what that entails for the determinatness of perfect games of finite length but with infinite action spaces of various cardinalities. Tijfo098 (talk) 06:23, 27 March 2011 (UTC)
 * I have responded at that article's talk page. --Trovatore (talk) 09:50, 27 March 2011 (UTC)

Something is wrong here...
There's considerable discussion here, so I'll try to keep this concise: tic tac toe is a game which is determined and where either neither player has a winning strategy, or (if winning is redefined to mean "not losing") both players have a winning strategy. But it's simple to define a game where a winning strategy is not possible: Consider a game where each player has one move, and that move is to determine if the other player wins. — Preceding unsigned comment added by 159.54.131.7 (talk) 14:58, 25 November 2011 (UTC)
 * I'll respond briefly, though technically, according to WP:TALK, we shouldn't be having this discussion here. If you need more detail, you can ask a question on WP:RD/Math.
 * The two points are separate, so let's treat them separately.
 * First, the axiom of determinacy in its usual form considers only games where there are no draws, so tic tac toe is out. It's easy to add considerations for draws, but you do have to make some small modifications.
 * Second, the game that you propose appears to be a win for the first player. Player I says "player II loses" and the game is over.  Or have I missed something?  You understand that the players can't both move at once, right? --Trovatore (talk) 19:35, 25 November 2011 (UTC)

Tweak recommended
This article uses that the plays are integers, but the article on Determinacy uses natural numbers. Seems like it would be good to be consistent, even if they are the logically the same.

--Thomaso (talk) 16:02, 11 July 2012 (UTC)
 * I suppose there's something to that. We don't normally work terribly hard to ensure consistency between articles, but there's no point in confusing readers just for the fun of it.
 * (By the way, I tried to look up the Mycielski–Steinhaus article and couldn't get it, but the abstract suggests that their games played 0 and 1 — also equivalent, though it's not quite as obvious.) --Trovatore (talk) 09:39, 12 July 2012 (UTC)

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Naming: Determinacy vs Determinateness
I have noticed that the original versions (Mostowski45, Mycielski64, Jech77, Herrlich06) talk of an axiom of determinateness. The only proper literature I found so far on axiom of determinacy is Jech05, there the author actually uses both names from what I dug up without a real preference or explanation of one over the other. Wouldn't the naming axiom of determinateness be more historically accurate? In my opinion it also makes it easier to distinguish between determinacy as a property of finite games and determinateness as an axiom of infinite games. Pinky Suavo (talk) 18:34, 21 March 2017 (UTC)
 * "Determinateness" is the older name, but in my experience that's not what people call it in more modern work. --Trovatore (talk) 19:50, 21 March 2017 (UTC)

Second proof of incompatibility with AC
Hello. I have added a second proof of incompatibility with AC. In my opinion, this addition adds to the article beyond the existing proof using the well-ordering of the continuum. (Speaking for myself only, I barely understand that proof.) This addition could make this article more understandable to non-experts. This has connections with other strategy-stealing arguments. My direct knowledge of this proof is from https://www.youtube.com/watch?v=Kj5RCs1FHcc (apologies if improper citation), a video by math PhD Youtube: SackVideo. (I otherwise do not know him.) He offered the citation "Proposition 28.1 of The Higher Infinite by Akihiro Kanamori," which I do not have access to. I quote Sack: "This argument actually shows something slightly stronger than AD and AC are incompatible: It shows that AD implies there are no non-principal ultrafilters over ω. (In the video, we use AC to construct a non-principal ultrafilter. However, the existence of a non-principal ultrafilter is weaker than AC.)" This could maybe be added to this article, but I will not do so due to lack of familiarity.

2600:1700:2CC1:6C20:7439:48EF:47E3:7A0A (talk) 19:10, 23 August 2023 (UTC)

Name for Vitali-type equivalence relation in second proof?
In the "2d proof" mentioned in the comment immediately above, added on 23 Aug 2023, I see this text:

 * Observe the equivalence relation on $$\{0, 1\}^\omega $$ such that two sequences are equivalent if and only if they differ in a finite number of terms. This partitions the set into equivalence classes, and let T be the set of equivalence classes (such that T has the cardinality of the continuum). Define $$\{0, 1\}^\omega \rightarrow T$$ that takes a sequence to its equivalence class.

Does this equivalence relation have a name? I realized earlier today that this equivalence relation is more or less exactly the same thing as the Vitali set. The correspondence is "obvious": The Vitali set asks you to consider equivalence classes of reals that differ by a rational. The above asks you to consider equivalence classes of reals that differ by a dyadic rational. But the rationals and the dyadic rationals are in one-to-one correspondence, via the Minkowski question mark function. So these are constructing the same thing.

Just to be extra-super clear about what I am saying, above: the $$\{0, 1\}^\omega $$ is of course the Cantor space, and it can be mapped onto the reals in the usual way, as infinite binary string expansions. Infinite binary strings that differ in a finite number of places map to reals that differ by a dyadic rational (since dyadic rationals are in one-to-one correspondence with finite-length binary strings.) So the equivalence relation is just $$\{0, 1\}^\omega / \mathbb{D}$$ with $$\mathbb{D}$$ the dyadic rationals, while the Vitali set is just $$\{0, 1\}^\omega / \mathbb{Q}$$ (and Vitali also asks you to pick one and only one representative from each equivalence class). And $$\mathbb{D}$$ and $$\mathbb{Q}$$ are in 1-1 correspondence via Minkowski question mark. There's a third article talking about this construction: the article on the infinite parity function describes the same thing (but badly) although it does mention there are uncountably many different infinite parity functions (one assignment per equivalence class).

So I am seeing this construction in three different articles in 24 hours, and I'm wondering "does it have a name"? In my mind, I'm going to call it a "Vitali-type construction" but this is my personal neologism. Can anyone do better? 67.198.37.16 (talk) 05:54, 28 November 2023 (UTC)
 * Yes, that equivalence relation (usually on $${}^\omega\omega$$ rather than $${}^\omega 2$$, but it doesn't make much difference) is known as $$E_0$$. It's very special in that it's the smallest Borel equivalence relation (in the order of Borel reducibility) that does not admit a Borel function giving a real-valued complete invariant for the equivalence relation.  See this paper by Harrington, Kechris, and Louveau. --Trovatore (talk) 08:15, 28 November 2023 (UTC)
 * Thank you! Perhaps it would be appropriate to start an article on $$E_0$$? Or more directly, I'd be interested in such an article, even if its a stub. 67.198.37.16 (talk) 21:05, 28 November 2023 (UTC)
 * "... that does not admit a Borel function giving a real-valued complete invariant for the equivalence relation." I assume that should read "in the standard model of the reals" since presumably one can still consistently assign it a measure of epsilon in non-standard analysis. But perhaps all of my comments should be moved to StackExchange, instead of here. Noted. 67.198.37.16 (talk) 14:35, 29 November 2023 (UTC)
 * This is an enjoyable discussion and I wish you'd ask a question on WP:RD/Math, where we could continue it. But briefly, no, nonstandard analysis has no loopholes to offer here. --Trovatore (talk) 17:22, 29 November 2023 (UTC)

 * I'll ask when I figure out what the question really is; I will need to do more reading. In the meanwhile, I will conclude that the relevant keywords are the Glimm-Effros dichotomy, the Feldman–Moore theorem and the Lusin–Novikov uniformization theorem, with at least two of those redlinks, if not all three, being redirects to Countable Borel relation which states them. 67.198.37.16 (talk) 19:13, 1 December 2023 (UTC)
 * Thanks for pointing me to that last article. The right division of labor for articles in this area is a little hard to work out.  I don't think I'd put so much of it into countable relations specifically (there's an article I started years ago on Borel equivalence relations, a little more than a stub, but I think it should probably host much of this content).  Anyway it sounds like I should get in touch with, except that he/she seems to have submitted that article for creation and then disappeared. --Trovatore (talk) 19:30, 1 December 2023 (UTC)
 * And while we're on the topic, the run-length encoding from Cantor space to Baire space, does it have a common name used in set theory? I call it "the Minkowski question mark function", because that is what it is after one projects Cantor/Baire down to the reals. But, before doing this projection, calling it the question mark is perhaps a mild neologism? 67.198.37.16 (talk) 22:29, 28 November 2023 (UTC)

Argh. Please excuse the rambling note; it's late-night and maybe I'm going batty; I keep wondering "where have I seen this before?" This Vitali-type construction is rampant in dynamical systems, isn't it? The generic case for discrete-time dynamical systems is that you have some time-step operator T and as it is iterated over time, it spits out a sequence of points $$x_1, x_2, \cdots$$ For large n, the generic cases are that either the $$x_n$$ settle down to a periodic orbit where they repeat, or they settle into a chaotic orbit given by some invariant measure. As a general rule, the pretense is to not care about the transient behavior, and only be interested in what the sequence is doing for large-n. So, for periodic orbits, you say "hey, consider the system that eventually settles down to a periodic orbit, and lump all the transients into an equivalence class, i.e. where eventually, the $$x_n$$ are all the same, except for a finite number of differences." Same deal for the chaotic orbits, although it is more subtle there. If the dynamical system is of a type where the $$x_n\in\{0,1\}$$, then the standard dynamical systems ploy of "just ignore the transients and lump them into an equivalence class" is exactly kind-of-ish this Vitali-set construction. Huh. And yeah, when a dynamical system has uncountably many of these equivalence classes, it is called an "anti-classification result" (because the hope of classifying behavior into a countable set of classes was dashed.) Anti-classification is not mysterious, though, it just says each different class is labeled by a single point in the Cantor set. Well, up to a finite number of differences. Huh. Who knew? Thank you for listening. I'm going to bed now, and will regret writing this the next morning. So it goes. 67.198.37.16 (talk) 08:10, 28 November 2023 (UTC)

 * Hi @Trovatore above you said "this is an enjoyable conversation"; sadly, I cannot continue it, my focus has gyrated to somewhere else. However, while closing out open browser tabs, I wanted to mention that I converted the above late-night ruminations into an 18-page PDF, here. It is an extended "homework exercise"; there is no ground-breaking content. I wanted to mention it as a closing remark. Unfortunately, I never had the chance to dig into Glimm–Effros dichotomy, etc. as I had hoped. Alas. Maybe later. 67.198.37.16 (talk) 18:31, 13 April 2024 (UTC)

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Wikipedia:Articles for deletion/Tim garton

Tim garton
"Tim Garton is the name of a boy currently in the 7th grade in Louisville, Kentucky."—a friend of the author's, apparently, and completely unverifiable. —No-One Jones (m) 17:57, 24 Oct 2004 (UTC)
 * Comment This article was deleted by User:The Anome. Content is as shown below. Reason not specified. I personally think it does qualify as a speedy under 2, newbie test, because even though it's long and elaborate I perceive these to be kids who are just playing with Wikipedia to see whether they could create this article, and at least borderline 4, vandalism, based on the comment "This site is supposed to be like an encyclopedia. I say screw that." This article did make me smile, though. [[User:Dpbsmith|Dpbsmith (talk)]] 21:11, 24 Oct 2004 (UTC) P. S. "The Catcher in the Rye!" Holden Caulfield! That's what it made me think of. [[User:Dpbsmith|Dpbsmith (talk)]] 21:13, 24 Oct 2004 (UTC)
 * Tim Garton is the name of a boy currently in the 7th grade in Louisville, Kentucky. He loves playing soccer—and is good at it too!—and is in A.P. He, along with 29 other selected kids, are in a class separate from the rest of his grade for doing good in math or something. The system is racist though. They mostly pick asians. I think that they were on crack when they picked ppl cuz they didn't do a very good job. He is on team 7-2 and is in Blizzards. He considers (or used to) himself a “jock”. He is sad about the death of Johnny Ramone. Words that he seems to say a lot are: “sweet”, “retarded”, “crazy”, “elaborate”, and he has been saying “f***” a lot recently. He has a brother in the 10th grade at duPont Manual High School, which is like a good school in the country. Tim’s middle school, Meyzeek Middle School, is a great school (I go there too!) and has many squirrels and frogs. But there is a girl named Marrina in his class that obviously likes him and is not very "achieving" if you know what i mean. She is a big flirt and is an idiotic, slutty, prep who thinks that she is the most popular and prettiest girl to ever live! She wears the ugliest effing red velvet sweat pants that I could barf on. And she wears the same Old Navy jeans like 3 times a week. Well, she’s another story. Tim would have better chance with any other girl in his class than Marrina! Tim listens to a variety of types of music. He sometimes reminds my friend of a guy named Kevin Sar in the 8th grade at Meyzeek, for his language, low voice, and hair style. Kevin Sar is an idiot too. He's too retarded to mention (no offense kevin....lol *cough*). Tim looks really bad when he puts his hair up in a ponytail. People claim he has a unibrow. I'm not so sure. All I know is that unibrows are weird and Tim looks weird when he pulls his bangs up. This site is supposed to be like an encyclopedia. I say screw that. No, jk. This is a cool site. For homework and stuff i guess. i sound corny.

Comment NSK (nsk2@wikinerds.org) has stated that Wikinerds, an all-encompassing "knowledge base" rather than an encyclopedia, is interested in having all VfD-ed articles resubmitted to them. I have already submitted this one to them. [[User:Dpbsmith|Dpbsmith (talk)]] 21:11, 24 Oct 2004 (UTC)


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User:Njaard

Wicked Cool Stuff
I was commended for tagging Winter as "needing attention." With Winter being my favorite season, it's only fitting. The article has truly blossomed beyond my wildest hopes and those that made the effort to improve it really deserve a nice cold beer.

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text: File:Melissa Etheridge Breakdown cover.jpg


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User talk:Slambo/Trains

According to the copy of the April 1984 Official Railway Equipment Register, there was exactly one class 1 railroad in Mexico, Ferrocarriles Nacionales de Mexico. There is also exactly one class 2 railroad listed there, Ferrocarril del Pacifico (although Texas Mexican is also listed there).

With so few railroads that would be listed on a Mexico class 1 or Mexico class 2 navigation template, it didn't seem prudent to create them yet. slambo 17:59, 24 Oct 2004 (UTC)

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text: Category:1987 singles

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text:
Aiguillon, Lot-et-Garonne

Aiguillon (Gulhon) is a commune of the Lot-et-Garonne department in southwestern France. It lies near the confluence of the rivers Lot and Garonne. Aiguillon station has rail connections to Agen, Langon and Bordeaux.

The organist and composer Marc de Ranse (1881–1951) was born in Aiguillon.

History
Attached to the English crown in 1318, it was conquered by Du Guesclin in 1370. The future Jean II conducted a large-scale but unsuccessful siege of the place in 1346. In 1599 it was converted into a duchy of its own.

title: Aiguillon, Lot-et-Garonne


text:
User:UHO Hi TZa LlI

STALK HER >>
Hello! Im Allison Lee, currently atteding La Mirada HS (2003-07). I have many hobbies, some of which include graphic designing (PS), movies, xanga, music, friends, im a shopaholic, i love sleep!! =80

< UPDATER more LATER >

title: User:UHO Hi TZa LlI


text:
Koca Sinan Pasha

Koca Sinan Pasha (Koca Sinan Paşa, "Sinan the Great", ; c. 1506 – 3 April 1596) was an Albanian-born Ottoman Grand Vizier, military figure, and statesman. From 1580 until his death he served five times as Grand Vizier.

Early life
Sinan Pasha, also known as Koca Sinan (Sinan the Great), was born in Topojan in Luma territory and was of Albanian origin. In a Ragusan document of 1571 listing members of the Ottoman Sultan's governing council, Sinan is described as coming from a Catholic family that converted to Islam. His father was named Ali Bey and Sinan Pasha had family ties with Catholic relatives such as the Giubizzas. Austrian orientalist Joseph von Hammer-Purgstall called him the "unbridled Albanian". Mustafa Ali of Gallipoli repeatedly criticized Sinan for promoting an Albanian clique in the administration.

Career
Sinan Pasha was appointed governor of Ottoman Egypt in 1569, and was subsequently involved until 1571 in the conquest of Yemen, becoming known as Fātiḥ-i Yemen ("Conqueror of Yemen").

In 1580, Sinan commanded the army against the Safavids in the Ottoman–Safavid War (1578–1590), and was appointed grand vizier by Sultan Murad III. Sinan was, however, disgraced and exiled in the following year, owing to the defeat of his lieutenant Mehmed Pasha, at Gori during an attempt to provision the Ottoman garrison of Tbilisi.

Sinan subsequently became governor of Damascus and, in 1589, after the great revolt of the Janissaries, was appointed grand vizier for the second time. He was involved in the competition for the throne in Wallachia between Mihnea Turcitul and Petru Cercel, and ultimately sided with the former, overseeing Petru's execution in March 1590. Another revolt of Janissaries led to his dismissal in 1591, but in 1593 he was again recalled to become grand vizier for the third time, and in the same year he commanded the Ottoman army in the Long War against the Habsburgs. He was faced with massive casualties on the northern front, which was weakened by the death of Bosnian commander Telli Hasan Pasha during the Battle of Sisak. In 1593, he captured Veszprém and Palota after 3–4 days of siege and turned his attention to the Sisak, where Telli Hasan Pasha and Ahmed Pasha had died. He soon captured Sisak and came back to Belgrade through Novi Sad.

When the Habsburgs invaded Szécsény and Nógrád he demanded help from Istanbul. The agha of Janissaries, Sokolluzade Lala Mehmed Pasha, came to help in a short time. Then he started besieging Györ (Yanuk) and captured the castle. In 1594 during the Uprising in Banat, Sinan ordered for the relics (remains) of Saint Sava to be brought from Mileševa to Belgrade, where he then had them set on fire in order to discourage the Serbs.

In spite of his victories he was again deposed in February 1595, shortly after the accession of Mehmed III, and banished to Malkara. In August, Sinan was in power again, called on to lead the expedition against Prince Michael the Brave of Wallachia. His defeat in the Battle of Călugăreni, the Battle of Giurgiu, and the series of unsuccessful confrontations with the Habsburgs (culminating in the devastating siege and fall of Ottoman-held Esztergom), brought him once more into disfavour, and he was deprived of the seal of office (19 November).

The death of his successor Lala Mehmed Pasha three days later caused Sinan to become grand vizier for the fifth time. He died suddenly in the spring of 1596, leaving behind a large fortune. Sinan Pasha is buried in Istanbul near the Grand Bazaar.

Family
He married Esmehan Hanımsultan, granddaughter of Sultan Selim I. They had a son, Mehmed Pasha, and three daughters, Emine Hanım, Hatice Hanım and Hüma Hanım.

Legacy
Sinan Pasha became grand vizier five times between 1580 and his death in 1596. He had many rivals but he was also a very wealthy man. During his lifetime Sinan Pasha was criticized by Ottoman bureaucrats such as Mustafa Âlî who wrote that Sinan promoted Albanians into the Ottoman government and military. Contemporary Turkish historians also note that he remained close to his heritage and would give those of Albanian stock preference for high-level positions within the empire. In 1586, at his request, Sultan Murad III issued a decree exempting five villages in Luma from all taxes. Sinan Pasha constructed the fortress of Kaçanik in the Kosovo Vilayet with an imaret (soup kitchen), two hans (Inn), a hamam (Turkish bath) and a mosque that still bears his name.

In 1590, he had the Pearl Kiosk built above the seaward walls on the sea of Marmara. It served as Murad III's final residence before his death. One of his final projects in Constantinople was a külliye completed in from 1593 to 1594 by Davut Aga, the chief imperial architect of the time. It is distinguished by the complex masonry and decorations of its türbe and sebil.

He was a major builder of caravanserais, bridges, baths and mosques. These included the town of Kaçanik in Kosovo, important buildings in Sarajevo, Thessalonika and Belgrade, as well as in Istanbul and other countries in the Arab world. He was a big supporter of Queen Mother Safiye Sultan who was also of Albanian origin

title: Koca Sinan Pasha


text:
Social Democrat Hunchakian Party

The Social Democrat Hunchakian Party (SDHP) (Սոցիալ Դեմոկրատ Հնչակյան Կուսակցություն; ՍԴՀԿ), is the oldest continuously-operating Armenian political party, founded in 1887 by a group of students in Geneva, Switzerland. It was the first socialist party to operate in the Ottoman Empire and in Iran, then known as Persia. Among its founders were Avetis Nazarbekian, Mariam Vardanian, Gevorg Gharadjian, Ruben Khan-Azat, Christopher Ohanian, Gabriel Kafian, and Manuel Manuelian. Its original goal was attaining Armenia's independence from the Ottoman Empire during the Armenian national liberation movement.

The party is also known as Hentchak, Henchak, Social-Democratic Hentchaks, Huntchakians, Hnchakian, Henchags, and its name is taken from its newspaper Hunchak, meaning "clarion" or "bell". This is taken by party members to represent "a call or awakening, for enlightenment and freedom".

History
All seven founders of the party were Eastern Armenian Marxist students who had left Russian Armenia to further their education in various universities of Western Europe. They were young, in their twenties, and supported by their affluent bourgeois families. They were influenced by social-democratic revolutionary ideology, contacted Frederick Engels, Georgi Plekhanov, and later Vladimir Lenin. Mariam Vardanian had worked with Russian revolutionaries in Saint Petersburg. For the purpose of furthering revolutionary activity in Turkish Armenia, they formed the Hunchakian Revolutionary Party in August, 1887. The party's manifesto, printed in the first issue of Hunchak journal, contained this slogan: "Those who cannot attain freedom through revolutionary armed struggle are unworthy of it". The Hunchak party fought many battles against the Ottoman Empire, to free the Armenian people from Turkish rule. During this period, many famous intellectuals joined Hunchakian party, including Smpad Piurad, Stepan Sapah-Gulian, Alexander Atabekian, Atrpet, and Aram Andonian. One of Armenia's famous national heroes Andranik Ozanian, at first, joined the Hunchak party, but disagreement with party policies led Andranik to leave the Hunchak ranks within less than a year, to join the Dashnaktsutyun party.

In the early days of the formation of Armenian political powers, the Dashnaktsutyun sought "reforms within the framework of the Ottoman Empire", while the Hunchakian party favored an independent Armenian state. Hunchak was the official organ of Hunchakians. In 1894, in Athens and London, the party published a socialist scientific monthly, Gaghapar, which for the first time published "The Communist Manifesto" in Armenian, translated by Avetis and Mariam Nazarbekians. The First General Conference of Hunchakian party took place in London, in September 1896.

In the Caucasus, the Hunchakian party has also played a prominent role, it combated the Russification policy of Viceroy Grigory Golitsyn, the Russian governor of Caucasus. In 1903, Paramaz organized the assassination attempt of Grigory Golitsyn. Paramaz was also one of the organizers of the self-defense troops during the Armenian-Tatar massacres of 1905–06.

The Hunchakian party was also active in the international socialist movement, and was represented at the 1904 congress of the Second International by Plekhanov.

Activities in the Ottoman Empire
On 27 July 1890, Hunchakian activists Harutiun Jangülian, Mihran Damadian, and Hambartsum Boyajian headed Kum Kapu Affray in Constantinople, which demanded the implementation of reforms in the Western Armenian provinces. In the early 1890s, frequent clashes between the Armenian inhabitants of Sason and the Turkish forces took place because of Sassontsis' refusal to pay retroactive taxes to the Turkish government. In 1894, Sasun Resistance was organized by the Hunchak party under the leadership of Mihran Damadian, Hambartsum Boyajian, Kevork Chavush, and Hrayr Dzhoghk.

In 1913, Hunchakian leader Paramaz participated in the 7th Conference of the Social Democrat Hunchakian Party in Constanta, where he represented the idea of the assassination of Ittihad leaders. But on 15 June 1915, Paramaz with 19 other his comrades were hanged in the central square of Constantinople.

 * Zeitun rebellion (1895–96) (October 1895 – January 1896)
 * Defense of Van: (June, 1896)
 * Khanasor Expedition: (July 25, 1897)
 * Zeitun Resistance: (August 30, 1914 – December 1, 1914 and March 25, 1915)
 * Siege of Van: (April 19, 1915 – May 6, 1915)
 * Shabin-Karahisar uprising: (June 2, 1915 – June 30, 1915)

First Republic of Armenia
The party also played a role in the establishment of the First Republic of Armenia, as party members took part in the Battle of Sardarapat in 1918, which defended the Armenian capital Yerevan from the Army of Islam of the Ottoman Empire.

Armenian Soviet Socialist Republic
After the takeover of the Armenian communists of power in Armenia in 1921 and dissolving of the Democratic Republic of Armenia, and the declaration of the Armenian Soviet Socialist Republic, all political parties apart from the Armenian Communist Party were forbidden. Thus the Social Democrat Hunchakian Party, alongside all the other Armenian traditional political parties, effectively became a party of the Armenian diaspora only.

But the party remained in general a supporter of the development of the Armenian SSR for many decades, in sharp contrast to the Armenian Revolutionary Federation (ARF) that remained opposed to the Communist regime in Armenia. This resulted at many times in feuds and rifts between the Hunchaks and the Dashnaks in many centers of the Armenian diaspora, a situation becoming worse with religious differences, with the Social Democrat Hunchakian Party supporting Mother See of Holy Etchmiadzin of the Armenian Apostolic Church and the ARF supporting the Holy See of Cilicia. In these conflicts, the Armenian Democratic Liberal Party (ADL) was seen as a political ally on the side of the SDHP and in opposition to the ARF.

Independent Armenia
Following Armenia's independence from the Soviet Union in 1991, Yeghia Najarian, headed the SDHP organization in Armenia and founded the "Hnchak Hayastani" official organ. In the early 1990s, the party took part in the self-defense of Zangezur (Paramaz battalion) and the Nagorno-Karabakh conflict (Jirair-Mourad battalion led by Gevorg Guzelian). The party also remains active throughout the Armenian Diaspora.

On 12 May 2024, members of the central committee of the party met with Armenian President Vahagn Khachaturyan in Los Angeles and discussed relevant political issues such as the demarcation of the Armenia–Azerbaijan border and cooperation with the Armenian diaspora in the United States. The central committee concluded the meeting by reaffirming their readiness to support Armenia's statehood and advance national priorities.

Activities in Lebanon
In the 1950s, the party clashed, sometimes violently, with the Dashnak Party, due to tensions that escalated when the ARF elected Bishop Zareh as Zareh I, Catholicos of Cilicia, a move that was rejected by the Hunchaks. This period was characterized by an escalation of conflict between the ARF on one side, and the SDHP and the ally ADL (Ramgavars) on the other side.

In the midst of increasing sectarian strife in the late 1960s and early 1970s, which led to the Lebanese Civil War, however, Lebanon's Armenian community began to close ranks, and in 1972, the Hunchakian Party ran a joint ticket with the Dashnaks. In 2000, the Hunchakian Party joined forces with Rafik Hariri's Future Movement, which swept the city of Beirut. SDHP Central Committee Member Dr Yeghia Jerejian was a member of Lebanese Parliament for many years.

The party subscribes to a socialist ideology and advocates for a planned economy in Lebanon. The party competes for the six seats reserved for ethnic Armenians in the National Assembly of Lebanon.

Ideology
The party declares itself as a national social democratic party. The party advocates for free education and healthcare, the promotion of human rights and equality, maintaining a strong democracy, protecting the environment, and creating a decentralized social economy. The party also supports the unification of Artsakh with Armenia.

In terms of foreign policy, the party supports Armenia developing closer cooperation within European structures, and developing closer ties with Georgia, Iran, China, and Japan. On 28 November 2023, the party announced its support for Armenia to join the European Union and to reduce its dependency on Russia.

Electoral record
The party was a previous member of the Armenian National Congress. Prior to the 2021 Armenian parliamentary election, the party announced that it would nominate 4 members to run in the elections under the Democratic Party of Armenia's electoral list. Following the election, the Democratic Party of Armenia won just 0.39% of the popular vote, failing to win any seats in the National Assembly. As such, the Social Democrat Hunchakian Party does not have any representation within the National Assembly of Armenia and currently acts as an extra-parliamentary force.

In June 2023, the Social Democrat Hunchakian Party and the European Party of Armenia formed an electoral alliance, known as Dignified Yerevan. The alliance nominated Karen Sargsyan as its candidate for the position of Mayor of Yerevan in municipal elections for September 2023. The alliance, however, dissolved in August 2023 prior to the elections.

Affiliate organizations
The Hunchakian party has established affiliate organizations such as the AEBU which is an organization that helps with educational, health and social care, the Dekhrouni Student & Youth Association (founded in 1952, in Beirut), the Gaidz Youth Organization (founded in 1910, in Constantinople), Nor Serount Cultural Association (founded in 1954, in Beirut), and HMM (Homenmen) which is an independent sporting organization but strongly affiliated with the SDHP (not to be confused with Homenetmen considered largely affiliated with the ARF).

Party publications
Hunchak (also Hnchak, Hentchak, "Bell" in Armenian) was the official organ of the party. It was founded by Avetis Nazarbekian and published originally in Geneva and later in Montpellier and Paris (France), Greece, London, and Providence (United States), 1887–1915, 1935–1940. The main purpose of the paper was a propaganda organ of the Armenian national movement for the liberation, the resistance in Western Armenian regions. Hunchak also supported the ideology of social-democracy and worker's consolidation.

Present-day party publications include:
 * Ararad daily newspaper published in Beirut, Lebanon
 * Tchahagir weekly published in Cairo, Egypt
 * Massis weekly and the online MassisPost published in Los Angeles
 * Nor Serounti Tsayn (Voice of the New Generation - Nor Serount) published in London, UK
 * Zank Armenian journal, Australia
 * Loussapatz, published monthly from Nor Serount Toronto, Canada

Recent developments
The party's 20th General Conference took place in September 2013, in Yerevan and Tsaghkadzor, with the participation of delegates from 17 countries.

The party's 22nd General Conference took place in September 2022, in Yerevan (coinciding with the 135th anniversary of the party's founding), with the participation of delegates from 14 countries.

Prominent members

 * Aghasi (Karapet Ter-Sargsian)
 * Alexander Atabekian
 * Aram Achekbashian
 * Avetis Nazarbekian
 * Ghazaros Aghayan
 * Girayr
 * Kegham Vanigian
 * Mari Beyleryan
 * Medzn Mourad
 * Paramaz
 * Sargis Mubayeajian
 * Sarkis Dkhrouni
 * Smpad Piurad
 * Stepan Sapah-Gulian
 * Shushanik Kurghinian

title: Social Democrat Hunchakian Party


text:
Barkhausen

Barkhausen is a German surname. Notable people with the surname include:

 * David N. Barkhausen (born 1950), American politician and lawyer
 * Heinrich Barkhausen (1881–1956), German physicist born at Bremen
 * Louis Henry Barkhausen (1877–1962), stamp collector of Chicago, Illinois

title: Barkhausen


text:
File:Eva Cassidy - Imagine.jpg

Cover for the album Imagine by Eva Cassidy

title: File:Eva Cassidy - Imagine.jpg


text: User talk:67.37.186.251

title: User talk:67.37.186.251


text:
Japanese aircraft carrier Taihō

Taihō (大鳳) was an aircraft carrier of the Imperial Japanese Navy during World War II. Possessing heavy belt armor and featuring an armored flight deck (a first for any Japanese aircraft carrier), she represented a major departure from prior Japanese aircraft carrier design and was expected to not only survive multiple bomb, torpedo, or shell hits, but also continue fighting effectively afterwards.

Built by Kawasaki at Kobe, she was laid down on 10 July 1941, launched almost two years later on 7 April 1943 and finally commissioned on 7 March 1944. She sank on 19 June 1944 during the Battle of the Philippine Sea due to explosions resulting from design flaws and poor damage control after suffering a single torpedo hit from the American submarine USS Albacore.

Design
Taihō was approved for construction in the 1939 4th Supplementary Programme. Her design was that of a modified Shōkaku-class aircraft carrier. Under the Modified Fleet Replenishment Program of 1942, Taihō was to be the first of a new generation of Japanese aircraft carriers, which would include Taihō, 15 of a modified JAPANESE AIRCRAFT CARRIER Hiryū design (which turned into the Unryū-class aircraft carrier) and five of an improved Taihō design (G-15 Project).

Hull
Taihō's waterline belt armor varied between 55 mm abreast the machinery to 152 mm around the magazines. The armor below the waterline was designed to withstand a 300 kg charge.

The weight of Taihō's armor immersed her hull so deeply that her lower hangar deck was barely above the load waterline and the bottoms of her two elevator wells (which formed the roofs of her fore and aft aviation fuel tanks) were actually below the waterline. This latter fact played an important role in her subsequent destruction during the Battle of the Philippine Sea.

Taihō's aviation fuel tanks were only partially protected with armor, as naval designers opted earlier to devote greater protection to their carriers' bomb and torpedo magazines. The empty air spaces around the aviation fuel tanks turned out to be the ship's downfall; all subsequent Japanese carriers had theirs filled with concrete to protect against splinters and shock damage, although it was poor damage control that ultimately sank Taihō.

To improve seakeeping and airflow over the forward end of the deck, Taihō's bow was plated up to flight deck level, giving her a similar appearance to British Illustrious-class aircraft carriers.

Machinery
Taihō's eight oil-fired Kampon RO-GO boilers were capable of generating 160000 shp. Her four Kampon steam turbines were each geared to separate propeller shafts. She had a top speed of 33.3 kn. Taihō's maximum fuel oil storage of 5700 ST gave her a radius of 10000 nmi at 18 kn.

Taihō had two rudders positioned along the longitudinal center-line of the ship: a semi-balanced main rudder (so-called because a portion of the rudder comes before the hinged axis and therefore requires less force to turn) located astern and an unbalanced auxiliary rudder forward of the main rudder. Both were turned via electro-hydraulically powered steering gears, but the auxiliary rudder could also be turned via a diesel engine in the event the primary steering gear was damaged.

Flight deck
Taihō was the first Japanese aircraft carrier to feature an armored flight deck, designed to withstand multiple 500 kg bomb hits with minimal damage. The armor varied slightly in thickness between 75 - 80 mm and formed a protective lid over an enclosed upper hangar whose sides and ends were unarmored. The floor of the upper hangar was also unarmored but the lower hangar deck had 32 mm plating. Taihō's flight deck, measuring 263 m long and 30 m wide, had the largest total area of any Japanese carrier until the completion of JAPANESE AIRCRAFT CARRIER Shinano and was offset 2 m to port to compensate for the weight of her island structure. Unlike all pre-war Japanese carriers, Taihō's flight deck was not wooden-planked. Rather, the steel deck was covered with a newly developed latex coating approximately 6 mm thick. This offered several advantages over wood: it was cheaper, it saved weight, it required fewer man-hours to apply and it was less likely to interfere with air operations in the event of minor damage. On the negative side, the material had only mediocre anti-skid qualities and tended to become brittle and crack over time.

Fourteen hydraulically operated arrester wires were distributed transversely across the flight deck between the fore and aft elevators. Taihō also had three hydraulically powered crash barriers, designed to abruptly stop any plane failing to catch an arrester wire upon landing. Two were located abreast the island and one was set at the bow. Taihō was equipped with two large 100 LT armored elevators, capable of transferring aircraft weighing up to 7.5 LT between decks. The elevators were widely spaced apart, with one at the far aft end of the ship and one forward of the island. It was originally desired to install a third elevator amidship, but because of wartime urgency this was deleted from the final design, thus saving both time and material. The elevators were roughly pentagonal in shape, with the aft elevator measuring 14 m long and 14 m wide. The forward elevator was slightly smaller in width. It took approximately 15 seconds to raise an aircraft from the lower hangar deck to the flight deck and the same to lower one.

Hangars
Taihō's upper and lower hangars were approximately 150 m long and 5 m high. The upper hangar was 1 m wider than the lower. Fighters were normally stowed in the middle and forward sections of the upper hangar and were raised to flight deck level using the bow elevator to facilitate more rapid handling. Dive bombers occupied the remaining upper hangar spaces with torpedo bombers stowed in the lower hangar. With greater all-up weights and longer take-off runs than the fighters, these planes were brought up to the flight deck using the aft elevator where they could then be spotted as far astern as possible.

As a fire safety precaution, the carrier's two hangars were divided into sections (five on the upper and four on the lower), separated by fire-proofed fabric curtains. The curtains were intended to limit the supply of air to and delay the spread of any fire breaking out on the hangar decks. Further protection against fire was supplied by a foam spray system fed by two rows of pipes and nozzles running along the walls and ends of the hangars. The lower hangar could also be flooded with carbon dioxide where the likelihood of fuel vapor build-up was greatest.

Taihō's original design specified installation of two catapults on her forward bow for power-assisted take-offs. However, as the Imperial Japanese Navy had not developed a workable catapult for carrier decks by the time of Taihō's construction, these were eventually deleted from the requirements. The IJN instead opted to use rocket-assisted take-off gear (RATOG) when necessary. This consisted of two solid-propellant (cordite) rockets attached to either side of a plane's fuselage. Generating 700 kgf of thrust for three seconds, they were able to get an aircraft airborne in a much shorter distance than normally required.

On Taihō's port side, abreast the aft elevator, stood a collapsible crane with a 4 LT lifting capacity. When not in use, it could be folded and lowered below flight deck level through an opening in the deck, thus eliminating a potentially hazardous obstruction during air operations.

Taihō's single large funnel, built into the island, was angled 26° from the vertical to starboard and carried the ship's exhaust gases well clear of the flight deck. This arrangement, atypical of most Japanese carriers, was similar to that successfully employed on JAPANESE AIRCRAFT CARRIER Junyō and JAPANESE AIRCRAFT CARRIER Hiyō and would later be repeated on JAPANESE AIRCRAFT CARRIER Shinano.

Three Type 96 searchlights were positioned along the outer edges of the flight deck: two on the port side and one to starboard, just aft of the island. Like the collapsible crane, these could be lowered below flight deck level to prevent interference with normal flight activity. A fourth searchlight was mounted to the starboard side of the carrier's island on a projecting sponson.

Armament
Taihō's armament comprised 12 of the brand-new 100 mm/65 caliber Type 98 anti-aircraft guns arranged in six twin-gun turrets: three on the port side and three to starboard. The guns were electro-hydraulically powered; however, in the event of a power failure they could function manually at reduced effectiveness. Operated by a crew of 11, the average firing rate was 15 rounds per minute with a maximum effective horizontal range of 14 km and a maximum effective vertical range of 11 km.

In addition, Taihō carried 17 triple-mount 25 mm anti-aircraft cannons (51 barrels total). Sixteen of these were mounted on sponsons just below flight deck level: eight to port, six to starboard and two at the stern. The 17th unit was positioned on the flight deck, just ahead of the island. The triple-mounts were electrically powered (though manual operation was possible) and normally required a crew of nine. They had a practical firing rate of 110–120 rounds per minute and a maximum effective range of 3 km. The 25 mm Type 96 cannon was the Japanese Navy's standard small-caliber anti-aircraft weapon from 1936 through the end of the war in 1945 and was an adaptation of a French design. Additionally, there were 25 portable Type 96 guns which were usually hung on hangar walls and after the plane departed were secured on metal fittings which usually held the aircraft on the deck.

Taihō had two Type 94 triaxially stabilized fire control directors, one mounted on the flight deck ahead of the island and one amidships on the port side, just below flight deck level. These controlled the 100 mm gun turrets and were electro-hydraulically powered. The 25 mm triple-mount cannons were controlled by seven Type 95 fire control units, each of which could direct the fire of two or three mounts.

Radar
Taihō's original design made no provisions for radar installation as the Imperial Japanese Navy did not possess any shipborne surface, fire control or air search radar at the war's outset in September 1939. Not until January 1941, when a Japanese naval technical mission arrived in Germany, did the IJN learn that European nations were using pulsed radar for combat purposes. In August that same year, the Navy Ministry initiated a crash plan to speed up radar development, resulting in (among others) the Type 21 and Type 13 air search radars.

Prior to completion in 1944, Taihō was fitted with two Type 21 air search radars, one mounted atop the island on the anti-aircraft control platform and one on the lower bridge deck at the aft end of the island. She also had one Type 13 air search set installed with an antenna mounted on the signal mast above the bridge. The Type 21 had a maximum effective range of 80 nmi while the Type 13 had a range of 54 nmi

Aircraft
Taihō's planned air complement varied considerably throughout her design and construction. Initially, it was envisioned she would carry 126 aircraft (with 30 of these in reserve). Later, this was pared down to 64, raised again to 78 and finally reduced to 53. One reason for the discrepancy in numbers was (in sharp contrast to the United States) the Imperial Japanese Navy's lack of insistence that its carrier planes have the smallest possible folded wingspan (many designs' folded only near the tips, while the wings of the Yokosuka D4Y Suisei dive-bomber did not fold at all). Her aircraft capacity was also changed based on previous wartime experience and the fact that Taihō was expected to carry larger newer-model carrier planes still under development at the time of her construction: 24 Mitsubishi A7M2 Reppu "Sam" fighters, 25 Aichi B7A2 Ryusei "Grace" torpedo-dive bombers and four Nakajima C6N1 Saiun "Myrt" reconnaissance planes. As none of these types were available at the time of her commissioning, Taihō went to sea with older-model aircraft.

Prior to 13 June 1944, Taihō carried 65 aircraft: 22 Mitsubishi A6M5 Reisen (Zero) fighters, 22 Yokosuka D4Y1 Suisei "Judy" dive bombers (of which four were the D4Y1-C reconnaissance types), three Aichi D3A2 "Val" dive bombers and 18 Nakajima B6N2 Tenzan "Jill" torpedo bombers. By 19 June 1944, however, the day the Battle of the Philippine Sea took place, she had already lost nine aircraft due to various causes and had just 56 planes remaining for actual combat.

Battle of the Philippine Sea
Taihō was formally commissioned on 7 March 1944. After several weeks of service trials in Japan's Inland Sea, she was deployed to Singapore, arriving there on 5 April. Taihō was then moved to Lingga Roads, a naval anchorage off Sumatra, where she joined veteran carriers JAPANESE AIRCRAFT CARRIER Shōkaku and JAPANESE AIRCRAFT CARRIER Zuikaku in the First Carrier Division, First Mobile Force. All three carriers engaged in working up new air groups by practicing launch and recovery operations and acting as targets for mock aerial attacks staged from Singapore airfields by their own planes. On 15 April, Vice-Admiral Jisaburo Ozawa officially transferred his flag from Shōkaku to Taihō to take advantage of the carrier's extensive command facilities. Shortly thereafter, the First Mobile Force departed Lingga and arrived on 14 May at Tawi-Tawi off Borneo, where the fleet could directly refuel with unrefined Tarakan Island crude oil and await execution of the planned Kantai Kessen ("decisive battle") known as Operation A-GO.

When American carrier strikes against the Marianas indicated an invasion of Saipan was imminent, the Japanese Combined Fleet staff initiated Operation A-GO on 11 June. Taihō and the rest of Ozawa's First Mobile Force departed Tawi-Tawi on 13 June, threading their way through the Philippine Islands and setting course for Saipan to attack American carrier forces operating in the vicinity.

Fate
On 19 June 1944, Taihō was one of nine Japanese aircraft carriers involved in the Battle of the Philippine Sea. At 07:45 she turned into the wind to launch her contribution (16 Zeros, 17 "Judy" dive bombers and 9 "Jill" torpedo bombers) to Ozawa's second attack wave. As Taihō's planes circled overhead to form up, American submarine USS Albacore (SS-218), which had spotted Ozawa's carriers earlier that morning, reached an ideal attack position and fired a spread of six torpedoes at the carrier. One of Taihō's strike pilots, Warrant Officer Sakio Komatsu, saw the torpedo wakes, broke formation and deliberately dived his plane into the path of one torpedo; the weapon detonated short of its target and four of the remaining five missed. The sixth torpedo, however, found its mark and the resulting explosion holed the carrier's hull on the starboard side, just ahead of the island. The impact also fractured the aviation fuel tanks and jammed the forward elevator between the flight deck and upper hangar deck.

With the ship down 1.5 m (5 ft) by the bows due to flooding, the forward elevator pit filled with a mixture of seawater, fuel oil and aviation gasoline, Taihō's captain marginally reduced her speed by a knot and a half to slow the ingress of seawater into the hull where the torpedo had struck. As no fires had started, Vice-Admiral Ozawa ordered that the open elevator well be planked over by a flight deck damage control party in order to allow resumption of normal flight operations. By 09:20 am, using wooden benches and tables from the petty officers' and sailors' mess rooms, this task was completed. Ozawa then launched two more waves of aircraft.

Meanwhile, leaking aviation gasoline accumulating in the forward elevator pit began vaporizing and the fumes soon permeated the upper and lower hangar decks. The crew recognised the danger but, through inadequate training, lack of practice or incompetence, their response was ineffectual. They bungled attempts to pump out the damaged elevator well, and failed to cover the fuel with foam from the hangar's fire suppression system.

Because Taihō's hangars were completely enclosed, mechanical ventilation was the only means of exhausting fouled air and replacing it with fresh air. Ventilation duct gates were opened on either side of hangar sections No. 1 and No. 2 and, for a time, the carrier's aft elevator was lowered to try to increase the draught. But this failed to have any appreciable effect and air operations were resumed about noon, requiring the elevator to be periodically raised as aircraft were brought up to the flight deck. In desperation, damage control parties used hammers to smash out the glass in the ship's portholes.

Sinking
Taihō's chief damage control officer eventually ordered the ship's general ventilation system switched to full capacity and, where possible, all doors and hatches opened to try to rid the ship of fumes. However, this just resulted in saturation of areas previously unexposed to the vapors and increased the chances of accidental or spontaneous ignition. About 14:30 that afternoon, 6½ hours after the initial torpedo hit, Taihō was jolted by a severe explosion. A senior staff officer on the bridge saw the flight deck heave up, and the sides of the ship blew out. Taihō dropped out of formation and began to settle in the water, clearly doomed. Though Admiral Ozawa wanted to go down with the ship, his staff prevailed on him to survive and to transfer his flag to the cruiser JAPANESE CRUISER Haguro. Taking the Emperor's portrait, Ozawa transferred to Haguro by destroyer. After he left, Taihō was torn by a second thunderous explosion and sank stern first at 16:28, taking 1,650 officers and men out of a complement of 2,150 down with her.

She sank at coordinates 12.08333°N, 138.2°W.

title: Japanese aircraft carrier Taihō


text:
User talk:Jensend

Welcome to the Wikipedia
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Feel free to contact me personally with any questions you might have. The Village pump is also a good place to go for quick answers to general questions. You can sign your name by typing 4 tildes, like this: ~.

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Sam [Spade] 18:06, 24 Oct 2004 (UTC)

title: User talk:Jensend


text:
Makkal Tamil Desam Katchi

Makkal Tamil Desam Katchi (People's Tamil Land Party, in Tamil: மக்கள் தமிழ் தேசம் கட்சி), generally just called Makkal Tamil Desam (MTD) is a political party in the Indian state of Tamil Nadu. MTD was founded on 22 August 2000. MTD has its base amongst the Yadava(Konar)(ietaiyar)ietaiyan) caste in the north and southern parts of the state. The Tamil Nadu Yadava Mahasabai supported the formation of the party. The party leader is S. Kannappan, a former All India Anna Dravida Munnetra Kazhagam (AIADMK) minister. Kannappan had been expelled from AIADMK before the foundation of MTD.

Ahead of the 2001 Tamil Nadu assembly elections MTD joined the National Democratic Alliance (NDA).

On 6 May 2002, the Puducherry unit of MTD broke away and joined Indian National Congress.

In the 2004 MTD took part in the People's Alliance, the third front in Tamil Nadu together with Janata Dal (United), Puthiya Tamizhagam and the Dalit Panthers of India. This front was basically formed by groups who were dissatisfied that Bharatiya Janata Party (BJP) had put NDA aside in Tamil Nadu and instead had launched a pure BJP-AIADMK front in the elections. MTD contested under the JD(U) symbol.

title: Makkal Tamil Desam Katchi


text: Category:Pashas

title: Category:Pashas