Question

How does Cantor's diagonal argument not contradict the well-ordering theorem?

score 116 · Answer 1 · 2021-06-27 07:22:20

116

Views

How does Cantor's diagonal argument not contradict the well-ordering theorem?

Published on 27 Jun 2021 - 7:22

score 167 · Answer 2 · 2021-06-28 14:15:15

167

Views

Without axiom of choice, how big can the product of a family be?

Published on 28 Jun 2021 - 14:15

score 174 · Answer 3 · 2021-07-04 16:59:44

174

Views

proof that a countable union of countable sets is countable, why is $\sf ZF$ not enough?

Published on 04 Jul 2021 - 16:59

score 260 · Answer 4 · 2026-03-27 16:28:07

260

Views

Where is the axiom of choice used in the measure-theoretic proof of the uncountability of $[0,1]$?

Published on 27 Mar 2026 - 16:28

score 79 · Answer 5 · 2026-04-03 22:59:05

79

Views

Adding the "Step-by-step injective extensions" axiom to ZF

Published on 03 Apr 2026 - 22:59

score 448 · Answer 6 · 2026-04-05 13:50:07

448

Views

The algebraic closure of the $p$-adic numbers and the axiom of choice

Published on 05 Apr 2026 - 13:50

score 136 · Answer 7 · 2021-07-23 01:11:42

136

Views

Does this proof of the existence of an injective function need the Axiom of Choice?

Published on 23 Jul 2021 - 1:11

score 223 · Answer 8 · 2021-07-23 16:50:31

223

Views

Can there be consistent countable FOL theories having no countable models?

Published on 23 Jul 2021 - 16:50

score 135 · Answer 9 · 2026-04-06 15:01:15

135

Views

Why does global choice imply a bijection between all proper classes?

Published on 06 Apr 2026 - 15:01

score 115 · Answer 10 · 2021-08-02 15:12:41

115

Views

Equivalent to the Axiom of Choice

Published on 02 Aug 2021 - 15:12

score 159 · Answer 11 · 2021-08-04 21:47:13

159

Views

Showing that $\mathsf{HOD}(\mathbb{R})$ always satisfies the axiom of countable choice

Published on 04 Aug 2021 - 21:47

score 104 · Answer 12 · 2026-04-01 00:25:24

104

Views

Fake proof of the Axiom of Specification

Published on 01 Apr 2026 - 0:25

score 143 · Answer 13 · 2026-04-06 16:57:07

143

Views

Use of the axiom of choice in a first course in ordinals

Published on 06 Apr 2026 - 16:57

score 59 · Answer 14 · 2021-08-18 16:57:43

59

Views

Can we get 'Transcendental Translates' without choice?

Published on 18 Aug 2021 - 16:57

score 118 · Answer 15 · 2021-08-19 07:26:20

118

Views

Heine's theorem and axiom of choice

Published on 19 Aug 2021 - 7:26

List Question

How does Cantor's diagonal argument not contradict the well-ordering theorem?

Without axiom of choice, how big can the product of a family be?

proof that a countable union of countable sets is countable, why is $\sf ZF$ not enough?

Where is the axiom of choice used in the measure-theoretic proof of the uncountability of $[0,1]$?

Adding the "Step-by-step injective extensions" axiom to ZF

The algebraic closure of the $p$-adic numbers and the axiom of choice

Does this proof of the existence of an injective function need the Axiom of Choice?

Can there be consistent countable FOL theories having no countable models?

Why does global choice imply a bijection between all proper classes?

Equivalent to the Axiom of Choice

Showing that $\mathsf{HOD}(\mathbb{R})$ always satisfies the axiom of countable choice

Fake proof of the Axiom of Specification

Use of the axiom of choice in a first course in ordinals

Can we get 'Transcendental Translates' without choice?

Heine's theorem and axiom of choice

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