User Asaf Karagila

8 votes

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Injection into a proper class and choice without regularity

answered Apr 25, 2019 at 23:20

8 votes

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Strong limit cardinals in AD

answered Dec 11, 2017 at 7:54

8 votes

Non smallness of the set of anafunctors without AC?

answered Mar 31, 2017 at 17:32

8 votes

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Does the partition principle imply (DC)?

answered Apr 13, 2022 at 13:56

8 votes

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Can Tychonoffs theorem for a countable number of spaces be proven with ZF plus the axiom of (countable) dependent choice?

answered Sep 10, 2021 at 12:01

8 votes

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What if $\mathbb{R}$ is in bijection with the cardinals less than $\frak{c}$?

answered Jun 24, 2019 at 10:15

8 votes

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Aronszajn Trees when AC fails

answered Jan 2, 2020 at 16:21

8 votes

When does Skolemization require the axiom of choice?

answered Dec 18, 2014 at 6:56

8 votes

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Relationship between fragments of the axiom of choice and the dependent choice principles

answered Aug 20, 2014 at 6:04

8 votes

On the difference between two concepts of even cardinalities: Is there a model of ZF set theory in which every infinite set can be split into pairs, but not every infinite set can be cut in half?

answered Dec 19, 2011 at 20:04

8 votes

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Countably generated $\sigma$-algebras of ${\mathcal P}({\mathbb R})$ and choice

answered Mar 24, 2012 at 0:52

8 votes

Which mathematicians have influenced you the most?

answered Jul 5, 2010 at 20:19

8 votes

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Does ZF bound countable unions of countable sets?

answered Oct 15, 2012 at 8:00

8 votes

Automorphisms of algebraically closed fields without the Axiom of Choice

answered Mar 9, 2023 at 14:24

7 votes

Is this version of Zorn's lemma provable in ZF?

answered 13 hours ago

7 votes

The Continuum Hypothesis and Countable Unions

answered Oct 18, 2012 at 13:42

7 votes

Does the fact that this vector space is not isomorphic to its double-dual require choice?

answered Apr 5, 2012 at 8:48

7 votes

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Distinguishing two local versions of the axiom of choice

answered Jul 17, 2012 at 21:14

7 votes

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Permutation models with a class-sized group

answered Dec 16, 2011 at 8:07

7 votes

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What sort of structure can amorphous sets support?

answered Jan 25, 2012 at 21:42

7 votes

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Is there an analogue of Shoenfield's absoluteness theorem, but for $\mathrm{On}$?

answered May 24, 2014 at 18:59

7 votes

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Are two forms of the Dual Schroeder-Bernstein property equivalent?

answered Jan 15, 2015 at 0:52

7 votes

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How big is the proper class of all sets?

answered Jun 29, 2013 at 11:39

7 votes

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A question about the first Cohen model

answered Jan 5, 2014 at 15:56

7 votes

Stationary sets and $\kappa$-complete normal ultrafilters

answered Jul 19, 2019 at 13:30

7 votes

Can Tychonoff's theorem be applied to topological spaces generated by program output in ZFC?

answered Mar 16, 2021 at 13:59

7 votes

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Does $|\kappa^{<\kappa}|=|\lambda^{<\lambda}|$ imply $\kappa=\lambda$?

answered Dec 29, 2021 at 14:43

7 votes

Terminology for a set that does not surject onto $\omega$ (in ZF)

answered Dec 4, 2021 at 19:15

7 votes

Proper class of inaccessibles and 1-inaccessible cardinals

answered Dec 30, 2022 at 20:26

7 votes

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Elementary countable submodels in Gödel's universe

answered Jan 11, 2023 at 15:57

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306 Answers

Injection into a proper class and choice without regularity

Strong limit cardinals in AD

Non smallness of the set of anafunctors without AC?

Does the partition principle imply (DC)?

Can Tychonoffs theorem for a countable number of spaces be proven with ZF plus the axiom of (countable) dependent choice?

What if $\mathbb{R}$ is in bijection with the cardinals less than $\frak{c}$?

Aronszajn Trees when AC fails

When does Skolemization require the axiom of choice?

Relationship between fragments of the axiom of choice and the dependent choice principles

On the difference between two concepts of even cardinalities: Is there a model of ZF set theory in which every infinite set can be split into pairs, but not every infinite set can be cut in half?

Countably generated $\sigma$-algebras of ${\mathcal P}({\mathbb R})$ and choice

Which mathematicians have influenced you the most?

Does ZF bound countable unions of countable sets?

Automorphisms of algebraically closed fields without the Axiom of Choice

Is this version of Zorn's lemma provable in ZF?

The Continuum Hypothesis and Countable Unions

Does the fact that this vector space is not isomorphic to its double-dual require choice?

Distinguishing two local versions of the axiom of choice

Permutation models with a class-sized group

What sort of structure can amorphous sets support?

Is there an analogue of Shoenfield's absoluteness theorem, but for $\mathrm{On}$?

Are two forms of the Dual Schroeder-Bernstein property equivalent?

How big is the proper class of all sets?

A question about the first Cohen model

Stationary sets and $\kappa$-complete normal ultrafilters

Can Tychonoff's theorem be applied to topological spaces generated by program output in ZFC?

Does $|\kappa^{<\kappa}|=|\lambda^{<\lambda}|$ imply $\kappa=\lambda$?

Terminology for a set that does not surject onto $\omega$ (in ZF)

Proper class of inaccessibles and 1-inaccessible cardinals

Elementary countable submodels in Gödel's universe