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Top Questions
18
votes
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
1
2
next
Top Answers
22
What notable theorems cannot be automatically proven without choice using Shoenfield absoluteness?
mathoverflow.net
13
Consistency of a strange (choice-wise) set of reals
mathoverflow.net
12
What are some reasonable-sounding statements that are independent of ZFC?
mathoverflow.net
12
Is this set theory equivalent to ZFC?
mathoverflow.net
12
Is every set being cardinal definable consistent with ZF + negation of Choice?
mathoverflow.net
12
Consistency of a strong Fubini type theorem for measure zero sets
mathoverflow.net
11
Is $\in$-induction provable in first order Zermelo set theory?
mathoverflow.net
11
Does ZF minus infinity imply collection?
mathoverflow.net
11
Can we prove the existence of $A\cup B$ without the union axiom?
math.stackexchange.com
11
How much choice is necessary to prove this statement?
mathoverflow.net
11
Is Global Choice conservative over Zermelo with Choice?
mathoverflow.net
10
Is "There exists an unbounded non-measurable set but no bounded non-measurable set" consistent with $\mathsf{ZF}$?
mathoverflow.net
9
Can one exhibit an explicit Kuratowski infinite set without invoking Replacement?
mathoverflow.net
9
Can we make ZF − infinity + “all ordinals are finite” as strong as ZFC?
mathoverflow.net
9
Example of a $\Pi^2_2$ sentence?
mathoverflow.net
9
Can a Vopenka cardinal be supercompact?
mathoverflow.net
8
Products of Cohen forcings
mathoverflow.net
8
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 $R_\theta$?
mathoverflow.net
7
Ideal-like filter on a ring not generated by ring ideals
mathoverflow.net
7
The Parity Principle and $\mathbf{C}_2$ (choice for $2$-sets)
mathoverflow.net
6
Stronger negation of AC given by rejecting "infinite hat" puzzles
mathoverflow.net
6
How hard is it to get "absolutely" no amorphous sets?
mathoverflow.net
5
Minimum number of axioms for ZFC set theory
math.stackexchange.com
5
Ordered pairs in NBG set theory
math.stackexchange.com
5
Does $\text{AC}_{\text{WO}}$ prove $\Theta \neq \aleph_{\omega+1}?$
mathoverflow.net
5
The difference between Baire 2 and 'effectively Baire 2'
mathoverflow.net
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