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I'm a graduate student at UC Berkeley, studying mathematical logic. I'm especially interested in reverse mathematics and abstract model theory.
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Sets of cardinalities of bases without choice
Oh, doy. OK, maybe I ought to be restricting attention to infinite cardinalities. :) 
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Sets of cardinalities of bases without choice
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Sets of cardinalities of bases without choice
That's nice! Yes, it does. (I've deleted my previous comments since they're no longer relevant.) I wonder if we can make it closed under finite intersections and finite unions? In general, I'm curious what's the "best" algebraic structure it can have? 
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asked  Sets of cardinalities of bases without choice 
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Math test and help
Please do not ask homework questions here. 
Apr 19 
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Prove that (AxB)∩(CxD)=(A∩C)x(B∩D)
Please do not ask homework questions here. 
Apr 18 
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Can we construct cohomolgy theory on noetherian separated schemes without Axiom of Choice?
"The one written in [book]" is far too broad (unless if a single theorem in the book fails to hold without choice, then you would say the answer is "no"). In order to make this an unambiguously real question, you have to actually tell us what you are asking: what results specifically do you want to remain true? In particular, your comment on David Speyer's answer (". . . affirmative or not . . .") implies that you're looking for a yes/no answer; but for such an answer to exist, you have to actually ask a yes/no question! 
Apr 18 
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Can we construct cohomolgy theory on noetherian separated schemes without Axiom of Choice?
Again, what do you mean by "the usual cohomology theory on schemes?" Do you have specific results in mind? "Cohomology theory" is very big! Certainly some results will require choice, and some results won't; what exactly are you asking about? 
Apr 17 
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Can we construct cohomolgy theory on noetherian separated schemes without Axiom of Choice?
(In particular, specifying what you are asking about  besides just being a good idea  will show that you've put serious thought into the question, and I suspect for a variety of reasons that doubt about this is part of the reason for the votes to close.) 
Apr 17 
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Can we construct cohomolgy theory on noetherian separated schemes without Axiom of Choice?
I'll point out the (very wellknown) fact that $\Pi^1_2$ sentences don't depend on AC, so any very concrete consequence of cohomological reasoning will not require choice to prove. But presumably you are interested in abstract results specifically about cohomology, which is again why you need to specify what exactly you want to do. 
Apr 17 
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Can we construct cohomolgy theory on noetherian separated schemes without Axiom of Choice?
Tl;dr version: if you don't want to ask "how much," then you have to specify what you want to "construct." 
Apr 17 
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Can we construct cohomolgy theory on noetherian separated schemes without Axiom of Choice?
First of all, I said this seems a real and appropriateforMO question if the question is "how much?." What I'm a little confused by is exactly what you mean by "Can we construct cohomology theory . . . " What would constitute a successful "construction?" For example, without choice, we can study whatever you like  injective resolutions, or wellorderings of the reals, or etc. Of course, in many cases our results will be different. So the meaning of the title question hinges on what you mean by "construct cohomology theory;" the "how much" version is more welldefined. 
Apr 17 
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Can we construct cohomolgy theory on noetherian separated schemes without Axiom of Choice?
I'm not entirely clear what the question in the OP is. If, however, it is "How much of the cohomology theory of noetherian separated schemes relies on AC?", this seems a real and appropriateforMO question. Or am I missing something? 
Apr 16 
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Why integer should have finite many digits?
This question is not appropriate for this site; however, you might be interested in $p$adic numbers, which can be thought of as allowing digits to run infinitely far to the left, but not the right: en.wikipedia.org/wiki/Padic_number. 
Apr 16 
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Why integer should have finite many digits?
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Apr 16 
answered  What year was Hechler forcing created? 
Apr 16 
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$\infty$Borel Determinacy?
A silly question: is it obvious that there is an $\infty$Borel set outside $L(\mathbb{R})$ (assuming, say, $ZF+AD+$"for every set of reals $A$, $\mathcal{P}(\mathbb{R})\not\subset L(\mathbb{R}, A)$)"? 
Apr 16 
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$\infty$Borel Determinacy?
@Carlo, I think that's exactly Andres' second comment. But thanks for the citation. 
Apr 16 
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$\infty$Borel Determinacy?
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Apr 16 
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$\infty$Borel Determinacy?
I didn't know that it was still open whether $AD$ proved "all sets of reals are $\infty$Borel," and it didn't occur to me that all sets of reals in $L(\mathbb{R})$ are $\infty$Borel; your two comments (as far as I'm concerned) completely answer question 1. 