Wikipedia:Articles for deletion/Axiom of global choice

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was nomination withdrawn. King of ♥ ♦ ♣ ♠ 05:18, 22 April 2013 (UTC)[reply]

Axiom of global choice

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Reason Eozhik (talk) 04:37, 21 April 2013 (UTC)[reply]

I nominated this article for deletion for the following reasons.

1) It does not contain references where its subject -- "axiom of global choice" -- is described: the texbooks by Kelley and by Jech given as references don't contain the term "axiom of global choice" at all.

2) I did not succeed independently in finding textbooks or papers where this term -- "axiom of global choice" -- is explained.

3) At the talk page of this article I suggested the authors to correct the references, but I did not receive a reasonable answer.

4) 7 months ago I initiated a trial at one of the websites for mathematicians, MathOverflow, http://mathoverflow.net/questions/107650/axiom-of-global-choice, about the content of this article in Wikipedia. My complaint was that the subject of the article resembles too much a hoax. Again, no reasonable answer followed.

I suppose this is enough for considering the necessity of deleting this article (and mentionings of the term "global choice" everywhere in Wikipedia). I don't exclude that the authors could rewrite this text in such a way that the idea of "global choice" could be endowed with some mathematical sense, but it's clear for me that something must be done with this.

I invite all authors (and readers) to share their opinion. Eozhik (talk) 04:37, 21 April 2013 (UTC)[reply]

Keep. Eozhik has misunderstood what Kelley (not Kelly!) says. I quote from p.273, "The following is a strong form of Zermelo's postulate or the axiom of choice. IX Axiom of choice. There is a choice function $c$ $c$ whose domain is ${\mathcal {U}}\sim \{0\}$ ${\mathcal {U}}\sim \{0\}$ " This is manifestly a statement of the axiom of global choice. - 振霖_T 09:31, 21 April 2013 (UTC)[reply]
- Indeed, "Kelley", I am sorry. I have corrected this. So you say, that Kelley's formulation is exactly what is called the "axiom of global choice"? Then why in the Wikipedia article it is called the "weak" form of the axiom of global choice? Eozhik (talk) 10:40, 21 April 2013 (UTC)[reply]
  - No, it isn't. Kelley's axiom is the second version: "V \ { ∅ } has a choice function (where V is the class of all sets; see Von Neumann universe)." - 振霖_T 11:02, 21 April 2013 (UTC)[reply]
    - ""Weak" form: Every class of nonempty sets has a choice function." -- this is from here: http://en.wikipedia.org/wiki/Axiom_of_global_choice. It is equivalent to Kelley's formulation, isn't it? So why "weak" here? Eozhik (talk) 11:12, 21 April 2013 (UTC)[reply]
    - If everything is so simple, why do people speak about the Grothendieck Universe when trying to explain this? Eozhik (talk) 13:07, 21 April 2013 (UTC)[reply]

Comment one of the comments in the mathoverflow discussion said it was referred to as the " global axiom of choice" a search for that yields a few hits ncatlab Foundations of Set Theory, A.A. Fraenkel, Y. Bar-Hillel, A. Levy, 1973, Page 133 and quite a few more.--Salix (talk): 09:47, 21 April 2013 (UTC)[reply]
- Thank you for the references. In Fraenkel-Bar-Hillel-Levy I indeed found the axiom of global choice. But note that in MathOverflow they did not give this reference. Eozhik (talk) 13:07, 21 April 2013 (UTC)[reply]

Keep As noted above, Eozhik appears to be confusing the axiom of global choice with the ordinary axiom of choice. It should not be surprising that some authors use "axiom of choice" to refer to what we call the global axiom of choice, but that does not make them the same thing. I put in the expression "weak form" to distinguish one version of the axiom of global choice from an apparently (but not actually) stronger version which has subsequently been removed from the article. Even what I called the weak form is stronger (really) than the ordinary axiom of choice. JRSpriggs (talk) 11:27, 21 April 2013 (UTC)[reply]
- In the present text the word "weak" confuses the reader. Because on reading this one gets an impression that what you call the "axiom of global choice" is actually stronger than what you call its "weak" form. Besides this, what is more important, there must be a reference to a source where this term "global choice" had been originally introduced, or at least described. There are no such references in the present version. Salix gave now a reference to the book by Fraenkel-Bar-Hillel-Levy, and only after that I got an opportunity to understand what one can have in mind when speaking about "global choice". These mistakes must be corrected. Eozhik (talk) 11:42, 21 April 2013 (UTC)[reply]

Keep: There are enough textbooks on this, just google books on it and you'll see: [1][2]. The current lack of references, or no answer upon questioning, isn't a strong reason to delete; the article has plenty of room to expand and include future refs, and is not in the way of anything. M∧Ŝc²ħεИ_τlk 11:47, 21 April 2013 (UTC)[reply]
- Among different textbooks there are some (actually, I now know only one, I have just learned about it due to Salix), where this term - "axiom of global choice" -- is explained, and there are others (in my impression, they form a majority), without this explanation. The mistake of the authors was that they chose wrong ones. Eozhik (talk) 12:16, 21 April 2013 (UTC)[reply]

Comment It is clear that the Axiom of Global Choice exists as a notable mathematical topic (try searching on ZMATH for example). It is equally clear that this article fails to explain it adequately and that the sources cited fail to support the article. Deltahedron (talk) 11:53, 21 April 2013 (UTC)[reply]

Speedy keep. The topic is clearly notable and not a hoax. Sławomir Biały (talk) 12:54, 21 April 2013 (UTC)[reply]
- If so, would you like to correct the mistakes? Eozhik (talk) 13:34, 21 April 2013 (UTC)[reply]
  - See WP:SOFIXIT. If you see mistakes, you should correct them. If you don't know how to fix them, you should ask on the discussion page of the article. Nominating an article for deletion is not an acceptable way to ask someone to fix the mistakes in an article. Sławomir Biały (talk) 21:06, 21 April 2013 (UTC)[reply]
Keep. Within ZFC, the global choice may be added in the form of the so-called Hilbert's global choice operator (used by Bourbaki, for example), giving ZGC. Boris Tsirelson (talk) 13:54, 21 April 2013 (UTC)[reply]

Keep, although I can't confirm the name. It's form E (attributed to Kurt Gödel in 1940) or CAC 1 in

Equivalents of the Axiom of Choice, II by H. Rubin and J. E. Rubin, Elsevier, 1985, ISBN 0-444-87708-8. One could argue that the first named form in a section of a reliable reference book is sufficiently notable. — Arthur Rubin (talk) 17:11, 21 April 2013 (UTC)[reply]

Comment According to the last phrase in Choice function#Bourbaki tau function it is mentioned by Hilbert in 1925 (earlier than Gödel 1940). Boris Tsirelson (talk) 17:54, 21 April 2013 (UTC)[reply]

Speedy Keep if the nominator wouldn't rather withdraw the nomination. Technical 13 (talk) 17:50, 21 April 2013 (UTC)[reply]

Note: This debate has been included in the list of Science-related deletion discussions. • Gene93k (talk) 21:04, 21 April 2013 (UTC)[reply]

OK, now the mistakes are corrected, so I have no further objections against the present text. I think only that it would be desireble to write simply that "usual choice" is for sets of sets, while "global choice" for classes of sets -- that would clarify everything from the very beginning. Anyway, I suppose I must do something to stop this discussion on the ground that the article took now an acceptable form. What should I do for this? Eozhik (talk) 23:51, 21 April 2013 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.