User Henry Towsner

76 votes

Accepted

How should a "working mathematician" think about sets? (ZFC, category theory, urelements)

answered Nov 28, 2016 at 18:12

38 votes

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How undecidable is the spectral gap?

answered Dec 12, 2015 at 2:49

33 votes

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Is there a computable ordinal encoding the proof strength of ZF? Is it knowable?

answered Apr 23, 2014 at 21:21

22 votes

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Why do stacked quantifiers in PA correspond to ordinals up to $\epsilon_0$?

answered Aug 11, 2013 at 2:05

16 votes

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What is the proof-theoretic ordinal of PA + Con(PA), PA + Con(PA + Con(PA)) etc., and why?

answered Jan 21, 2014 at 23:59

15 votes

Consistency of Analysis (second order arithmetic)

answered Mar 8, 2014 at 14:34

15 votes

Birkhoff ergodic theorem and the measure of the bad points

answered Aug 25, 2013 at 21:06

13 votes

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Nontrivial upper bounds on proof-theoretic ordinals of strong theories: do we have any?

answered Mar 9, 2014 at 0:18

13 votes

Is it possible for P(N) to be larger than Aleph_omega?

answered Mar 10, 2011 at 1:50

13 votes

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Natural examples of Reverse Mathematics outside classical analysis?

answered Nov 1, 2014 at 19:25

13 votes

Why is there a need for ordinal analysis?

answered Dec 4, 2015 at 16:25

11 votes

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Correspondence between proof-theoretic ordinals and fast growing functions?

answered Jun 11, 2018 at 21:48

10 votes

Does formalizing math require search and creativity, or is it near-mechanical?

answered May 15, 2014 at 12:49

10 votes

What notions are used but not clearly defined in modern mathematics?

answered Feb 26, 2011 at 4:06

9 votes

Accepted

Does second-order arithmetic prove every expressible instance of Dependent Choice?

answered Sep 18, 2010 at 7:42

9 votes

Understanding the nature and structure of proofs; Reverse Mathematics and Proof Theory. Prerequisites? Good introductory texts?

answered Jan 12, 2013 at 16:34

9 votes

Which ordinals can be proof-theoretic ordinals of a reasonable theory?

answered Oct 27, 2014 at 22:45

9 votes

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Notable examples of syntactic proofs whose existence is guaranteed by completeness, but having been found later than a semantic proof?

answered Jul 19, 2017 at 13:58

9 votes

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Reasoning Using Countable Subsets of Real Numbers

answered Feb 20, 2018 at 15:01

8 votes

How to construct a constructive proof from a non-constructive proof using prime ideals?

answered Sep 14, 2016 at 16:47

8 votes

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Which ordinals are proof-theoretic ordinals?

answered Jul 11, 2015 at 19:20

8 votes

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Models of PRA/EFA with induction on $X$ but not $\omega^X$

answered Jun 3, 2014 at 4:39

8 votes

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An interpretation of not-Con(PA)

answered Sep 25, 2014 at 16:43

8 votes

Accepted

Admissible ordinal beyond $\omega_{1}^{ck} .$

answered Jun 9, 2012 at 21:43

8 votes

Why is "P vs. NP" necessarily relevant?

answered Feb 3, 2011 at 22:18

7 votes

Interpretation of the Second Incompleteness Theorem

answered Sep 9, 2010 at 20:18

7 votes

AC and Euclidean Geometry

answered Jan 15, 2013 at 19:34

7 votes

what are the proof-theoretic ordinals of second-order arithmetic and ZFC?

answered Mar 24, 2014 at 23:15

7 votes

What ordinals are definable relations in Peano Arithmetic?

answered Nov 1, 2012 at 17:22

7 votes

Natural $\Pi^1_2$ (or worse) classes of structures?

answered Oct 28, 2013 at 17:45

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68 Answers

How should a "working mathematician" think about sets? (ZFC, category theory, urelements)

How undecidable is the spectral gap?

Is there a computable ordinal encoding the proof strength of ZF? Is it knowable?

Why do stacked quantifiers in PA correspond to ordinals up to $\epsilon_0$?

What is the proof-theoretic ordinal of PA + Con(PA), PA + Con(PA + Con(PA)) etc., and why?

Consistency of Analysis (second order arithmetic)

Birkhoff ergodic theorem and the measure of the bad points

Nontrivial upper bounds on proof-theoretic ordinals of strong theories: do we have any?

Is it possible for P(N) to be larger than Aleph_omega?

Natural examples of Reverse Mathematics outside classical analysis?

Why is there a need for ordinal analysis?

Correspondence between proof-theoretic ordinals and fast growing functions?

Does formalizing math require search and creativity, or is it near-mechanical?

What notions are used but not clearly defined in modern mathematics?

Does second-order arithmetic prove every expressible instance of Dependent Choice?

Understanding the nature and structure of proofs; Reverse Mathematics and Proof Theory. Prerequisites? Good introductory texts?

Which ordinals can be proof-theoretic ordinals of a reasonable theory?

Notable examples of syntactic proofs whose existence is guaranteed by completeness, but having been found later than a semantic proof?

Reasoning Using Countable Subsets of Real Numbers

How to construct a constructive proof from a non-constructive proof using prime ideals?

Which ordinals are proof-theoretic ordinals?

Models of PRA/EFA with induction on $X$ but not $\omega^X$

An interpretation of not-Con(PA)

Admissible ordinal beyond $\omega_{1}^{ck} .$

Why is "P vs. NP" necessarily relevant?

Interpretation of the Second Incompleteness Theorem

AC and Euclidean Geometry

what are the proof-theoretic ordinals of second-order arithmetic and ZFC?

What ordinals are definable relations in Peano Arithmetic?

Natural $\Pi^1_2$ (or worse) classes of structures?