User Ali Enayat

10 votes

Can a countable union of two-element sets be uncountable?

answered Feb 11, 2022 at 18:22

9 votes

Reference for precise form of Mostowski: “sets correspond to rooted, well-founded, extensional graphs”?

answered Jul 6, 2023 at 11:43

9 votes

Accepted

Can two set theories extending Z be different and yet bi-interpretable?

answered Jun 19, 2018 at 11:04

9 votes

Accepted

History of forcing over admissible sets

answered Dec 23, 2016 at 7:50

9 votes

Accepted

What is the proof-theoretic ordinal of bare $\mathsf{NFU}$?

answered Apr 1, 2021 at 20:53

9 votes

Set theory determined by $V_\alpha$ for limit ordinals $\alpha>\omega$

answered Jan 17, 2022 at 23:50

9 votes

Connectedness of the complement of small subsets (extended question)

answered Jan 3, 2013 at 6:39

9 votes

Boolean Valued Models of PA

answered Oct 13, 2014 at 12:24

9 votes

Accepted

How long can it take to generate a $\sigma$-algebra?

answered May 8, 2013 at 21:30

8 votes

Does ZFC prove the universe is linearly orderable?

answered Oct 27, 2012 at 18:32

8 votes

Accepted

Vaught's conjecture for partial orders

answered Feb 18, 2014 at 19:39

8 votes

Accepted

How do you prove that Q+Con(PA) can't be interpreted in ACA_0?

answered Mar 28, 2014 at 0:18

8 votes

Accepted

When was Bounded Zermelo set theory first formulated?

answered Nov 18, 2014 at 16:54

8 votes

End Extension models of $I\Delta_0$

answered Dec 4, 2015 at 15:32

8 votes

Height of ordered set

answered Jul 26, 2011 at 2:24

8 votes

Generalising Vitali Sets to uncountable dense subgroup selectors...

answered Jul 8, 2011 at 21:01

8 votes

Ordinal set $\Omega$ : von Neumann definition and modern definition

answered May 31, 2011 at 13:43

8 votes

Algebraic structures of greater cardinality than the continuum?

answered Jun 2, 2011 at 14:26

8 votes

Was Cantor aware of Lebesgue theory of integration?

answered Oct 19, 2020 at 15:29

8 votes

Is there a theory in a finite language that is computably axiomatizable but not by a finite number of axiom schemas?

answered Jun 20, 2020 at 15:06

8 votes

Does foundation/regularity have any categorical/structural consequences, in ZF?

answered May 17, 2018 at 2:47

8 votes

Is this theory synonymous with PA?

answered Jan 5 at 10:24

8 votes

Accepted

How often are forcing extensions of countable computably saturated models of $\mathsf{ZFC}$ computably saturated?

answered May 4, 2022 at 3:54

8 votes

Accepted

Forcing a unique $\Delta_3^1$ generic real

answered Apr 15, 2023 at 23:12

7 votes

Dedekind-Peano axioms, but numbers have at most one successor

answered Jan 22, 2023 at 11:38

7 votes

Accepted

Existence of a particular function that maps an arbitrary set of ordinals to a single ordinal

answered Jun 28, 2022 at 12:01

7 votes

Measure of the numbers with length of $n$ for a nonstandard number $n$

answered Feb 17, 2019 at 13:27

7 votes

Accepted

Are there ill-founded "maximally wide" models of $\mathsf{ZFC}$?

answered Jul 19, 2021 at 22:42

7 votes

Accepted

Higher-order preservation theorems?

answered Jun 9, 2011 at 21:10

7 votes

Accepted

ordered fields with the bounded value property

answered Jul 27, 2011 at 22:25

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126 Answers

Can a countable union of two-element sets be uncountable?

Reference for precise form of Mostowski: “sets correspond to rooted, well-founded, extensional graphs”?

Can two set theories extending Z be different and yet bi-interpretable?

History of forcing over admissible sets

What is the proof-theoretic ordinal of bare $\mathsf{NFU}$?

Set theory determined by $V_\alpha$ for limit ordinals $\alpha>\omega$

Connectedness of the complement of small subsets (extended question)

Boolean Valued Models of PA

How long can it take to generate a $\sigma$-algebra?

Does ZFC prove the universe is linearly orderable?

Vaught's conjecture for partial orders

How do you prove that Q+Con(PA) can't be interpreted in ACA_0?

When was Bounded Zermelo set theory first formulated?

End Extension models of $I\Delta_0$

Height of ordered set

Generalising Vitali Sets to uncountable dense subgroup selectors...

Ordinal set $\Omega$ : von Neumann definition and modern definition

Algebraic structures of greater cardinality than the continuum?

Was Cantor aware of Lebesgue theory of integration?

Is there a theory in a finite language that is computably axiomatizable but not by a finite number of axiom schemas?

Does foundation/regularity have any categorical/structural consequences, in ZF?

Is this theory synonymous with PA?

How often are forcing extensions of countable computably saturated models of $\mathsf{ZFC}$ computably saturated?

Forcing a unique $\Delta_3^1$ generic real

Dedekind-Peano axioms, but numbers have at most one successor

Existence of a particular function that maps an arbitrary set of ordinals to a single ordinal

Measure of the numbers with length of $n$ for a nonstandard number $n$

Are there ill-founded "maximally wide" models of $\mathsf{ZFC}$?

Higher-order preservation theorems?

ordered fields with the bounded value property