Question

There is no surjective function from a set in the Hartogs number of its power set

score 132 · Answer 1 · 2023-09-05 10:00:39

132

Views

There is no surjective function from a set in the Hartogs number of its power set

Published on 05 Sep 2023 - 10:00

score 70 · Answer 2 · 2023-09-08 07:12:00

70

Views

Does the proof that "a proper ascending chain of subsets of the naturals is countable" necessitate axiom of choice?

Published on 08 Sep 2023 - 7:12

score 161 · Answer 3 · 2023-09-12 18:23:51

161

Views

Maximal ideal theorem in Heyting Algebras implies choice

Published on 12 Sep 2023 - 18:23

score 87 · Answer 4 · 2023-09-17 13:32:45

87

Views

Axiom of Choice / Lemma 8.4.5 in Terence Tao Analysis I

Published on 17 Sep 2023 - 13:32

score 150 · Answer 5 · 2023-09-19 11:25:12

150

Views

What does it mean to explicity exhibit something (modulo a proof of its existence) which cannot be explicitly exhibited?

Published on 19 Sep 2023 - 11:25

score 37 · Answer 6 · 2023-09-19 12:46:05

37

Views

Is the axiom of choice used to order the orbits of the truncation function through periodic 2-adic numbers using their Lyndon words?

Published on 19 Sep 2023 - 12:46

score 315 · Answer 7 · 2023-09-22 15:06:07

315

Views

Is the axiom of choice needed to show that the initial topology is a topology?

Published on 22 Sep 2023 - 15:06

score 153 · Answer 8 · 2023-09-27 20:46:20

153

Views

Understanding a world without the axiom of choice (AOC)

Published on 27 Sep 2023 - 20:46

score 79 · Answer 9 · 2026-03-27 12:27:31

79

Views

Linear ordering of reals in Cohen's first model

Published on 27 Mar 2026 - 12:27

score 71 · Answer 10 · 2026-03-27 12:28:58

71

Views

Necessity of Axiom of Choice for unordered pairs of real subsets.

Published on 27 Mar 2026 - 12:28

score 87 · Answer 11 · 2023-10-10 00:40:24

87

Views

Proof verification: these two notions of AoC are equivalent.

Published on 10 Oct 2023 - 0:40

score 119 · Answer 12 · 2023-10-17 13:17:16

119

Views

Is this explanation of a wrong proof of AC correct?

Published on 17 Oct 2023 - 13:17

score 84 · Answer 13 · 2023-10-23 20:51:12

84

Views

Second power of an infinite set is Dedekind-infinite

Published on 23 Oct 2023 - 20:51

score 115 · Answer 14 · 2026-03-28 12:13:23

115

Views

Can Hilbert projection theorem be proved without AC?

Published on 28 Mar 2026 - 12:13

score 91 · Answer 15 · 2023-10-28 06:18:25

91

Views

Can I avoid using the axiom of choice to solve 3-13? (Michael Spivak's "Calculus on Manifolds")

Published on 28 Oct 2023 - 6:18

List Question

There is no surjective function from a set in the Hartogs number of its power set

Does the proof that "a proper ascending chain of subsets of the naturals is countable" necessitate axiom of choice?

Maximal ideal theorem in Heyting Algebras implies choice

Axiom of Choice / Lemma 8.4.5 in Terence Tao Analysis I

What does it mean to explicity exhibit something (modulo a proof of its existence) which cannot be explicitly exhibited?

Is the axiom of choice used to order the orbits of the truncation function through periodic 2-adic numbers using their Lyndon words?

Is the axiom of choice needed to show that the initial topology is a topology?

Understanding a world without the axiom of choice (AOC)

Linear ordering of reals in Cohen's first model

Necessity of Axiom of Choice for unordered pairs of real subsets.

Proof verification: these two notions of AoC are equivalent.

Is this explanation of a wrong proof of AC correct?

Second power of an infinite set is Dedekind-infinite

Can Hilbert projection theorem be proved without AC?

Can I avoid using the axiom of choice to solve 3-13? (Michael Spivak's "Calculus on Manifolds")

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