User Ali Enayat

47 votes

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What axioms are used to prove Gödel's Incompleteness Theorems?

answered Jan 6, 2013 at 8:06

31 votes

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Do the analogies between metamathematics of set theory and arithmetic have some deeper meaning?

answered Dec 30, 2015 at 10:01

27 votes

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

answered Jul 25, 2011 at 20:28

24 votes

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Classifying set theories whose standard models sharing the same ordinals are equal

answered Dec 17, 2014 at 20:38

23 votes

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Similarities between Post's Problem and Cohen's Forcing

answered Mar 8, 2013 at 21:02

23 votes

Can we find strong fixed-points in the fixed-point lemma of Gödel's incompleteness theorem, that is, where the fixed point is syntactically identical to its substitution instance rather than merely provably equivalent to it?

answered Apr 11, 2012 at 1:43

23 votes

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Forcing over set theory versus forcing over arithmetic

answered Jun 28, 2012 at 1:24

23 votes

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Must uncountable standard models of ZFC satisfy CH?

answered Jan 31, 2022 at 7:10

21 votes

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A contradiction in the Set Theory of von Neumann–Bernays–Gödel?

answered Apr 11, 2023 at 1:56

21 votes

Half Cantor-Bernstein without choice

answered May 18, 2011 at 22:32

21 votes

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Is there an $L$ like inner model for $\sf Z$?

answered Oct 25, 2014 at 14:41

20 votes

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Non-standard models of finite set theory

answered May 4, 2011 at 14:15

20 votes

What flavor of set theory is used in model theory?

answered Jan 28, 2022 at 4:39

18 votes

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SPOT as a conservative extension of Zermelo–Fraenkel

answered Aug 5, 2021 at 15:42

18 votes

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Does ZF(C) prove countable reflection?

answered Jan 23, 2022 at 4:38

18 votes

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Von Neumann's consistency proof

answered Nov 20, 2014 at 11:16

17 votes

Topological characterization of the closed interval $[0,1]$

answered Mar 6, 2013 at 18:24

17 votes

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Kunen's inconsistency result

answered Feb 27, 2013 at 4:45

17 votes

Dedekind's theorem

answered Jun 17, 2011 at 15:32

16 votes

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Alternative Arithmetics

answered Jun 2, 2011 at 23:28

16 votes

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Set theory inside arithmetics via the Ackermann yoga

answered Jun 7, 2011 at 17:03

16 votes

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Heights of well-founded parts of models of $\mathsf{ZFC}$

answered Dec 23, 2020 at 22:38

16 votes

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Is there an uncountable Borel almost disjoint family?

answered Jan 15, 2016 at 17:20

16 votes

Is Global Choice conservative over Zermelo with Choice?

answered Mar 20, 2019 at 8:52

16 votes

Set-theoretical foundations of Mathematics with only bounded quantifiers

answered Apr 7, 2019 at 21:08

15 votes

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van der Waerden's theorem in Reverse Mathematics

answered Nov 29, 2018 at 11:56

15 votes

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The (non-)absoluteness of second-order elementary equivalence

answered Mar 28, 2014 at 10:27

14 votes

What are the models of Peano Arithmetic plus the negation of the corresponding Gödel sentence like?

answered May 30, 2011 at 20:03

14 votes

Completeness vs Compactness in logic

answered Jun 26, 2011 at 21:09

14 votes

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What axioms are stronger than the Axiom of choice?

answered Jan 1, 2013 at 18:15

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126 Answers

What axioms are used to prove Gödel's Incompleteness Theorems?

Do the analogies between metamathematics of set theory and arithmetic have some deeper meaning?

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

Classifying set theories whose standard models sharing the same ordinals are equal

Similarities between Post's Problem and Cohen's Forcing

Can we find strong fixed-points in the fixed-point lemma of Gödel's incompleteness theorem, that is, where the fixed point is syntactically identical to its substitution instance rather than merely provably equivalent to it?

Forcing over set theory versus forcing over arithmetic

Must uncountable standard models of ZFC satisfy CH?

A contradiction in the Set Theory of von Neumann–Bernays–Gödel?

Half Cantor-Bernstein without choice

Is there an $L$ like inner model for $\sf Z$?

Non-standard models of finite set theory

What flavor of set theory is used in model theory?

SPOT as a conservative extension of Zermelo–Fraenkel

Does ZF(C) prove countable reflection?

Von Neumann's consistency proof

Topological characterization of the closed interval $[0,1]$

Kunen's inconsistency result

Dedekind's theorem

Alternative Arithmetics

Set theory inside arithmetics via the Ackermann yoga

Heights of well-founded parts of models of $\mathsf{ZFC}$

Is there an uncountable Borel almost disjoint family?

Is Global Choice conservative over Zermelo with Choice?

Set-theoretical foundations of Mathematics with only bounded quantifiers

van der Waerden's theorem in Reverse Mathematics

The (non-)absoluteness of second-order elementary equivalence

What are the models of Peano Arithmetic plus the negation of the corresponding Gödel sentence like?

Completeness vs Compactness in logic

What axioms are stronger than the Axiom of choice?