User Noah Schweber

88 votes

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What does it mean to suspect that two conjectures are logically equivalent?

answered Oct 23, 2017 at 19:37

77 votes

What are some important but still unsolved problems in mathematical logic?

answered Dec 27, 2015 at 19:10

64 votes

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How can I improve my formal definitions?

answered Aug 29, 2019 at 21:16

47 votes

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Hilbert's alleged proof of the Continuum Hypothesis in "On the Infinite"

answered Jun 12, 2017 at 16:51

47 votes

Why not adopt the constructibility axiom $V=L$?

answered May 20, 2019 at 3:33

43 votes

What are some deep theorems, and why are they considered deep?

answered Aug 16, 2013 at 20:01

43 votes

The error in Petrovski and Landis' proof of the 16th Hilbert problem

answered Jun 17, 2014 at 4:03

41 votes

Zorn's lemma: old friend or historical relic?

answered Dec 11, 2022 at 21:15

34 votes

Circular, or missing, definition in set theory?

answered May 21, 2018 at 20:59

32 votes

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Can we take a supremum over all Hilbert spaces?

answered Nov 5, 2020 at 22:45

31 votes

What are some examples of theorem requiring highly subtle hypothesis?

answered Jun 1, 2020 at 6:36

30 votes

Are there proofs that you feel you did not "understand" for a long time?

answered May 17, 2013 at 3:25

27 votes

What is the most useful non-existing object of your field?

answered Sep 28, 2014 at 22:20

25 votes

Are there first-order statements that second order PA proves that first order PA does not?

answered Jul 26, 2020 at 0:14

24 votes

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Do we expect that sufficiently large computable ordinals settle every question of arithmetic?

answered Oct 15, 2022 at 0:09

24 votes

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Can we interpret arithmetic in set theory, with exactly PA as the ZFC provable consequences?

answered May 26, 2022 at 0:14

23 votes

Do Grothendieck universes matter for an algebraic geometer?

answered May 13, 2019 at 17:26

23 votes

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Hard-to-compute real numbers

answered Oct 21, 2016 at 14:44

22 votes

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Has the exponentiation of ordinals a nice geometric model?

answered Apr 24, 2020 at 20:12

21 votes

What are some deep theorems, and why are they considered deep?

answered Aug 16, 2013 at 20:20

20 votes

For a computable binary tree, is having no computable branches the same as having no probabilistic algorithm for producing branches?

answered Dec 30, 2017 at 15:11

19 votes

Are there 'finitistic' nonrecursive functions (assuming Church's Thesis is false)?

answered Mar 9, 2016 at 20:03

18 votes

Similarities between Post's Problem and Cohen's Forcing

answered Mar 8, 2013 at 21:30

18 votes

Consistency results separating three cardinal characteristics simultaneously

answered Feb 4, 2014 at 3:24

18 votes

Why can we assume a ctm of ZFC exists in forcing

answered Jun 5, 2022 at 19:53

18 votes

A Löwenheim–Skolem–Tarski-like property

answered Nov 21, 2023 at 19:57

18 votes

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Cantor-Bernstein with "weakly injective" functions

answered Feb 4 at 17:54

17 votes

Paradoxical Mathematical Objects Pending for Construction

answered Aug 12, 2018 at 20:31

16 votes

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Road to Solovay's Land.

answered Aug 11, 2012 at 1:53

16 votes

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Computable models of the ordinal numbers

answered Sep 9, 2019 at 2:52

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451 Answers

What does it mean to suspect that two conjectures are logically equivalent?

What are some important but still unsolved problems in mathematical logic?

How can I improve my formal definitions?

Hilbert's alleged proof of the Continuum Hypothesis in "On the Infinite"

Why not adopt the constructibility axiom $V=L$?

What are some deep theorems, and why are they considered deep?

The error in Petrovski and Landis' proof of the 16th Hilbert problem

Zorn's lemma: old friend or historical relic?

Circular, or missing, definition in set theory?

Can we take a supremum over all Hilbert spaces?

What are some examples of theorem requiring highly subtle hypothesis?

Are there proofs that you feel you did not "understand" for a long time?

What is the most useful non-existing object of your field?

Are there first-order statements that second order PA proves that first order PA does not?

Do we expect that sufficiently large computable ordinals settle every question of arithmetic?

Can we interpret arithmetic in set theory, with exactly PA as the ZFC provable consequences?

Do Grothendieck universes matter for an algebraic geometer?

Hard-to-compute real numbers

Has the exponentiation of ordinals a nice geometric model?

What are some deep theorems, and why are they considered deep?

For a computable binary tree, is having no computable branches the same as having no probabilistic algorithm for producing branches?

Are there 'finitistic' nonrecursive functions (assuming Church's Thesis is false)?

Similarities between Post's Problem and Cohen's Forcing

Consistency results separating three cardinal characteristics simultaneously

Why can we assume a ctm of ZFC exists in forcing

A Löwenheim–Skolem–Tarski-like property

Cantor-Bernstein with "weakly injective" functions

Paradoxical Mathematical Objects Pending for Construction

Road to Solovay's Land.

Computable models of the ordinal numbers