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May
5
answered A sufficient condition for a probability measure to have compact support
Apr
29
comment the topology of power series ring
A naive question: what is DVR?
Apr
26
comment “Axiom of global choice”
Joel, I understand that the choice for classes is stronger than the choice for sets, there is no need to persuade me. But (logically) this doesn't mean that everybody must use different names for these two axioms. There is some per cent of people (and I belonged to them) who (after reading Kelley) believe that there is just one axiom of choice, the axiom for classes of sets, and the other its formulations (for sets of sets, for countable sets of sets, etc.) are just special cases. For those people it was impossible to understand what was written in that Wikipedia article before 21/04/2013.
Apr
24
comment “Axiom of global choice”
"I would regard it as a mistake to refer to both axioms as the "axiom of choice"" - however, Kelley and many others do this in their texbooks. On reading that article in Wikipedia (the version of 7 months ago) one could think that a great theory was invented, an extension of Gödel-Bernays, something indeed powerful, which allows to operate with "conglomerates of classes"! Who could expect that the explanation of that peal will be so banal - just terminology: we'll just call this special version of choice a "global choice", and everybody is free to think what he wants about "conglomerates"!
Apr
24
comment “Axiom of global choice”
And, Joel, I don't agree with you that this is completely standard material. I was also studying logic at the university in Moscow, and I never met the term "global choice". What Fraenkel, Bar-Hillel and Levy call "global choice" our professors (and the authors of the books we were reading) called just "choice". To say nothing about "conglomerates of classes".
Apr
24
comment “Axiom of global choice”
The more so that even specialists can't explain some details in those hints. For example, I would be very grateful to you, if you could add also some references where the term which attracted me from the very beginning is explained -- the "conglomerates of classes". It was mentioned in the Wikipedia article 7 months ago when I created this thread, and for me, an external observer, the impression was that it is exactly "global choice" which describes the properties of those "conglomerates". But up to now nobody explained the meaning of this term.
Apr
24
comment “Axiom of global choice”
Joel, when making impression of this topic I followed the references of the article in Wikipedia devoted to this "Axiom of global choice". That was before 21/04/2013 when I initiated that investigation on whether this term indeed has sense. There were only two textbooks there, namely, By Jech and by Kelley. None of them contains this term "global choice". My idea was that when people explain something mathematical it is their duty to provide the reader the necessary references, it's not the reader who must catch their hints.
Apr
22
awarded  Popular Question
Apr
21
comment “Axiom of global choice”
doesn't matter!
Apr
21
comment “Axiom of global choice”
Asaf, you exaggerate my ignorance. The problem was that instead of writing simply and clearly that "usual choice" is for sets of sets, while "global choice" is for classes of sets, they pretended that there is a "more powerful choice" for "collections of classes" or for "conglomerates of classes" – that was the main puzzle, and finally it turned out to be a hoax. The aim of my initiative in Wikipedia now was to force them to throw away any rudiments of these sermons. And they did it at last. –
Apr
21
comment “Axiom of global choice”
@Asaf: In Wikipedia en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/… they have just explained me that "axiom of global choice" is exactly what Kelley calls "axiom of choice". It is a great surprise for me that people used to divide this general result into classes of special statements depending on different "Universes".
Apr
21
comment “Axiom of global choice”
Appendix of SGA? What is it? In which translation is this? English?
Apr
21
revised “Axiom of global choice”
added 1211 characters in body
Apr
20
comment “Axiom of global choice”
As far as I understand, $U$ must be a set here, is it? If yes, then I don'see any profits. If the "axiom of global choice" is just the usual axiom of choice applied to families of $U$-classes (which are families of sets), then why do people introduce the very term "axiom of global choice", and claim that "the axiom of global choice is a stronger variant of the axiom of choice which applies to proper classes as well as sets" (en.wikipedia.org/wiki/Axiom_of_global_choice). This is evidently not true in the situation you describe.
Apr
17
comment Is rigour just a ritual that most mathematicians wish to get rid of if they could?
This sounds strange. I wonder, this discussion, where was it? :)
Apr
14
awarded  Critic
Apr
13
comment “Axiom of global choice”
Actually, I even can't find this term at all, "global axiom of choice", in textbooks. I used to think that axiom of choice can be applied to classes of sets, I never saw other versions of this trick, so what you write is completely unfamiliar for me.
Apr
13
comment “Axiom of global choice”
Which text namely?
Apr
13
comment “Axiom of global choice”
I am afraid, this is too technical for me. Are you saying that it is possible to extend the Gödel-Bernays theory in such a way that the axiom of choice becomes more powerful, it can be applied to classes?
Apr
13
comment “Axiom of global choice”
Dimitri, is it possible to translate this into the language of the Gödel-Bernays set theory?