Elliot Glazer

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Do choice principles in all generic extensions imply AC in $V$?

set-theory forcing axiom-of-choice asked Jul 31, 2018 at 17:58

mathoverflow.net

13 votes

Does Foundation increase the strength of second-order logic?

set-theory lo.logic higher-order-logics asked Jun 1, 2018 at 20:45

mathoverflow.net

11 votes

Does $\text{AC}_{\text{WO}}$ prove $\Theta \neq \aleph_{\omega+1}?$

set-theory axiom-of-choice cardinal-arithmetic asked Nov 17, 2020 at 5:12

mathoverflow.net

10 votes

Is $V=L$ equivalent to there being a $\Sigma_1$ well-ordering of the universe?

set-theory descriptive-set-theory asked Aug 7, 2017 at 21:18

mathoverflow.net

9 votes

How many iterations of inner models/generic extensions are sufficient?

set-theory forcing asked May 28, 2018 at 3:59

mathoverflow.net

9 votes

Definitional complexity of truth in $L$ without $0^{\#}$

set-theory asked May 8, 2017 at 16:00

mathoverflow.net

8 votes

Models of ZF with more elements than ordinals

set-theory asked Apr 22, 2017 at 2:49

math.stackexchange.com

7 votes

Is there an algorithm for extending a complete set theory to one with classes?

set-theory asked May 18, 2018 at 2:20

math.stackexchange.com

7 votes

A theory which seems to have proof-theoretic ordinal $\omega_1^{CK}$

logic computability proof-theory asked Nov 9, 2018 at 10:00

math.stackexchange.com

7 votes

Can $V$ only have well-orderings definable with respect to a parameter?

set-theory asked Jan 10, 2016 at 21:59

math.stackexchange.com

Top Answers

What notable theorems cannot be automatically proven without choice using Shoenfield absoluteness?

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Consistency of a strange (choice-wise) set of reals

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What are some reasonable-sounding statements that are independent of ZFC?

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Is this set theory equivalent to ZFC?

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Is every set being cardinal definable consistent with ZF + negation of Choice?

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Consistency of a strong Fubini type theorem for measure zero sets

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Is $\in$-induction provable in first order Zermelo set theory?

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Does ZF minus infinity imply collection?

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Can we prove the existence of $A\cup B$ without the union axiom?

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How much choice is necessary to prove this statement?

mathoverflow.net

Is Global Choice conservative over Zermelo with Choice?

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Is "There exists an unbounded non-measurable set but no bounded non-measurable set" consistent with $\mathsf{ZF}$?

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Can one exhibit an explicit Kuratowski infinite set without invoking Replacement?

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Can we make ZF − infinity + “all ordinals are finite” as strong as ZFC?

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Example of a $\Pi^2_2$ sentence?

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Can a Vopenka cardinal be supercompact?

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Products of Cohen forcings

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If $A, B$ is a non-trivial partition of $S^1$, is it possible that $R_\theta(A) \cap B$ has measure zero for all rotations $R_\theta$?

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Ideal-like filter on a ring not generated by ring ideals

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The Parity Principle and $\mathbf{C}_2$ (choice for $2$-sets)

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Stronger negation of AC given by rejecting "infinite hat" puzzles

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How hard is it to get "absolutely" no amorphous sets?

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Minimum number of axioms for ZFC set theory

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Ordered pairs in NBG set theory

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Does $\text{AC}_{\text{WO}}$ prove $\Theta \neq \aleph_{\omega+1}?$

mathoverflow.net

The difference between Baire 2 and 'effectively Baire 2'

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