User Asaf Karagila

16 votes

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Is it consistent that $|[\kappa]^{<\kappa}| > \kappa$?

answered Feb 18, 2019 at 13:36

16 votes

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Cardinalities of which there exists partitions of a set containing elements of the same size

answered Feb 12, 2018 at 18:18

16 votes

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BCT equivalent to DC

answered Oct 3, 2020 at 12:47

15 votes

Sheaf-theoretic approach to forcing

answered Mar 4, 2021 at 11:21

15 votes

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Examples of vector spaces with bases of different cardinalities

answered Aug 18, 2021 at 15:08

15 votes

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Is there a more modern account of the main results of "Adding Dependent Choice" by D. Pincus?

answered Oct 31, 2022 at 9:40

15 votes

Ultrafilters and diagonal arguments

answered Apr 6, 2018 at 22:02

15 votes

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Can $\mathbb{R}$ be partitioned into dedekind-finite sets?

answered Feb 9, 2014 at 5:31

15 votes

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Difference between ZFC and ZF+GCH

answered Oct 31, 2014 at 14:53

15 votes

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Axiom of choice and bases of vector spaces over a fixed field

answered Jun 27, 2011 at 20:23

15 votes

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Mathematics with the negation of AC

answered Jan 22, 2013 at 14:11

15 votes

Not especially famous, long-open problems which higher mathematics beginners can understand

answered Feb 22, 2013 at 23:27

14 votes

Counterintuitive consequences of the Axiom of Determinacy?

answered Apr 28, 2013 at 22:50

14 votes

Are there examples of statements that have been proven whose consistency proofs came before their proofs?

answered Jul 25, 2011 at 22:58

14 votes

Most memorable titles

answered May 8, 2011 at 14:59

14 votes

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Notions of infinity in $\mathsf{ZF}$ without choice

answered Mar 30, 2015 at 7:38

14 votes

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Pathological behavior of Borel sets?

answered Apr 7, 2014 at 23:21

14 votes

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Is not SH + not CH consistent?

answered Aug 9, 2014 at 10:24

14 votes

Elementary+Short+Useful

answered Dec 19, 2013 at 23:10

14 votes

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Does the existence of a unique chromatic (possibly transfinite) number for every (possibly non-finite) simple graph imply the axiom of choice?

answered Apr 13, 2018 at 15:30

14 votes

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Can we have an infinite sequence of decreasing cardinality all terms of which have equal sized power sets?

answered Aug 12, 2018 at 14:59

14 votes

Continuous linear functionals and the Axiom of Choice

answered Oct 14, 2021 at 21:22

14 votes

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Intuition about ordinal fixed points $\alpha = \aleph_\alpha$

answered Jul 7, 2020 at 16:57

13 votes

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Does every countable set of Turing degrees have an upper bound, without AC?

answered Apr 19, 2021 at 18:12

13 votes

Wiki for consequences of axiom of choice?

answered Oct 10, 2020 at 16:53

13 votes

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Axiom(s) of choice and bases of vector spaces

answered Sep 10, 2017 at 10:07

13 votes

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Relationship between AC, WO, and Zorn's lemma in ZF-Powerset

answered Apr 26, 2019 at 10:10

13 votes

Consistency of a non-measurable set of reals when the continuum cannot be well-ordered

answered Dec 24, 2017 at 14:36

13 votes

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Is $\mathbb{R}$ a $\mathbb{C}$-module without AC?

answered Sep 18, 2014 at 7:52

13 votes

ZF + the reals are the countable union of countable sets consistent

answered Jun 26, 2012 at 22:33

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296 Answers

Is it consistent that $|[\kappa]^{<\kappa}| > \kappa$?

Cardinalities of which there exists partitions of a set containing elements of the same size

BCT equivalent to DC

Sheaf-theoretic approach to forcing

Examples of vector spaces with bases of different cardinalities

Is there a more modern account of the main results of "Adding Dependent Choice" by D. Pincus?

Ultrafilters and diagonal arguments

Can $\mathbb{R}$ be partitioned into dedekind-finite sets?

Difference between ZFC and ZF+GCH

Axiom of choice and bases of vector spaces over a fixed field

Mathematics with the negation of AC

Not especially famous, long-open problems which higher mathematics beginners can understand

Counterintuitive consequences of the Axiom of Determinacy?

Are there examples of statements that have been proven whose consistency proofs came before their proofs?

Most memorable titles

Notions of infinity in $\mathsf{ZF}$ without choice

Pathological behavior of Borel sets?

Is not SH + not CH consistent?

Elementary+Short+Useful

Does the existence of a unique chromatic (possibly transfinite) number for every (possibly non-finite) simple graph imply the axiom of choice?

Can we have an infinite sequence of decreasing cardinality all terms of which have equal sized power sets?

Continuous linear functionals and the Axiom of Choice

Intuition about ordinal fixed points $\alpha = \aleph_\alpha$

Does every countable set of Turing degrees have an upper bound, without AC?

Wiki for consequences of axiom of choice?

Axiom(s) of choice and bases of vector spaces

Relationship between AC, WO, and Zorn's lemma in ZF-Powerset

Consistency of a non-measurable set of reals when the continuum cannot be well-ordered

Is $\mathbb{R}$ a $\mathbb{C}$-module without AC?

ZF + the reals are the countable union of countable sets consistent