Question

How many nonprincipal ultrafilters exists on $X$ such that $|X|^2=|X|$?

score 151 · Answer 1 · 2021-02-07 21:24:03

151

Views

How many nonprincipal ultrafilters exists on $X$ such that $|X|^2=|X|$?

Published on 07 Feb 2021 - 21:24

score 114 · Answer 2 · 2021-02-08 14:36:37

114

Views

Disjointness in proof of Tarski's Theorem that $|X\times X|=|X|$ for all infinite sets implies Choice

Published on 08 Feb 2021 - 14:36

score 116 · Answer 3 · 2026-04-06 10:20:14

116

Views

In $\mathsf{ZF}$, for each set $A$ exists an ordinal $\alpha$ such that no surjection $A\to \alpha$ exists

Published on 06 Apr 2026 - 10:20

score 58 · Answer 4 · 2026-04-03 16:27:27

58

Views

uses and proofs of the cardinality of the continuum

Published on 03 Apr 2026 - 16:27

score 129 · Answer 5 · 2021-02-16 00:49:27

129

Views

Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?

Published on 16 Feb 2021 - 0:49

score 170 · Answer 6 · 2021-02-16 15:48:54

170

Views

Axiom of choice equivalence

Published on 16 Feb 2021 - 15:48

score 88 · Answer 7 · 2026-03-29 05:50:09

88

Views

Does this simple proof use the axiom of choice?

Published on 29 Mar 2026 - 5:50

score 89 · Answer 8 · 2026-03-29 20:02:26

89

Views

Weird cofinality behavior without choice?

Published on 29 Mar 2026 - 20:02

score 58 · Answer 9 · 2021-02-20 16:41:52

58

Views

Strengthening of the axiom of Dependent Choice

Published on 20 Feb 2021 - 16:41

score 475 · Answer 10 · 2021-02-21 17:52:25

475

Views

Axiom of Choice and Completeness of the Reals

Published on 21 Feb 2021 - 17:52

score 39 · Answer 11 · 2021-02-21 19:39:21

39

Views

An example of a class of structures whose axiomatizability depends on the axiom of choice

Published on 21 Feb 2021 - 19:39

score 216 · Answer 12 · 2021-02-24 13:37:31

216

Views

Help with the proof of Zorn's Lemma: if $A$ and $B$ are conforming subsets, why must it be that $A\subseteq B$ or $B\subseteq A$?

Published on 24 Feb 2021 - 13:37

score 66 · Answer 13 · 2021-02-25 13:42:11

66

Views

Can a partially ordered set $D$ have a function that maps every chain to a strict upper bound?

Published on 25 Feb 2021 - 13:42

score 280 · Answer 14 · 2021-02-27 03:46:43

280

Views

In ZF, if injection from A to B doesn't exist, then does surjection from A to B exist?

Published on 27 Feb 2021 - 3:46

score 84 · Answer 15 · 2021-02-27 17:01:23

84

Views

Finite axiom of choice in Munkres

Published on 27 Feb 2021 - 17:01

List Question

How many nonprincipal ultrafilters exists on $X$ such that $|X|^2=|X|$?

Disjointness in proof of Tarski's Theorem that $|X\times X|=|X|$ for all infinite sets implies Choice

In $\mathsf{ZF}$, for each set $A$ exists an ordinal $\alpha$ such that no surjection $A\to \alpha$ exists

uses and proofs of the cardinality of the continuum

Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?

Axiom of choice equivalence

Does this simple proof use the axiom of choice?

Weird cofinality behavior without choice?

Strengthening of the axiom of Dependent Choice

Axiom of Choice and Completeness of the Reals

An example of a class of structures whose axiomatizability depends on the axiom of choice

Help with the proof of Zorn's Lemma: if $A$ and $B$ are conforming subsets, why must it be that $A\subseteq B$ or $B\subseteq A$?

Can a partially ordered set $D$ have a function that maps every chain to a strict upper bound?

In ZF, if injection from A to B doesn't exist, then does surjection from A to B exist?

Finite axiom of choice in Munkres

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