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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”
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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?
Apr
11
comment Algebraic description of compact smooth manifolds?
Excuse me, is it possible to reformulate the conclusions of this theory for the question that Jason DeVito asked? Which properties distinguish $C^\infty(M)$ among other $\Bbb R$-algebras?
Apr
8
comment “Axiom of global choice”
Dimitri, I did not undertand you. Is this written anywhere? If not, can you contact me to explain what you write? (Or explain this here.)
Mar
31
revised Naive question about the representation theory of algebraic groups and hopf algebras
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Mar
31
revised Naive question about the representation theory of algebraic groups and hopf algebras
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Mar
31
revised Naive question about the representation theory of algebraic groups and hopf algebras
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Mar
31
answered Naive question about the representation theory of algebraic groups and hopf algebras
Jan
21
comment Is the Mendeleev table explained in quantum mechanics?
Uwe, thank you for the support.