Question

Does the existence of a function in this proof require the axiom of choice?

score 49 · Answer 1 · 2020-11-03 19:20:35

49

Views

Does the existence of a function in this proof require the axiom of choice?

Published on 03 Nov 2020 - 19:20

score 479 · Answer 2 · 2026-04-05 20:15:56

479

Views

Riemann integrable function is bounded, without any type of choice

Published on 05 Apr 2026 - 20:15

score 97 · Answer 3 · 2020-11-08 13:33:16

97

Views

Is there a uniform way to define an upper bound on $|X|$ union of $|X|$-sized sets in ZF?

Published on 08 Nov 2020 - 13:33

score 31 · Answer 4 · 2026-04-06 05:18:53

31

Views

Can ZF prove the cartesian product of an ordinal by itself to be subnumerous to that ordinal?

Published on 06 Apr 2026 - 5:18

score 69 · Answer 5 · 2026-04-06 05:18:54

69

Views

Can $\omega_2$ be the order type of a countable union of countable sets of ordinals?

Published on 06 Apr 2026 - 5:18

score 45 · Answer 6 · 2020-11-10 13:20:00

45

Views

Reference Request: On the proof of $H(x)$ sets in ZF?

Published on 10 Nov 2020 - 13:20

score 36 · Answer 7 · 2020-11-12 11:48:39

36

Views

Does this basic cardinal inequality require the axiom of choice?

Published on 12 Nov 2020 - 11:48

score 151 · Answer 8 · 2026-03-29 18:36:24

151

Views

Existence of a generic filter $G$ such that $p\in G$ and Axiom of choice

Published on 29 Mar 2026 - 18:36

score 58 · Answer 9 · 2026-03-29 07:40:25

58

Views

If $R$ is noetherian then every family $\mathcal{C}$ of ideals in $R$ has a maximal element in $\mathcal{C}.$

Published on 29 Mar 2026 - 7:40

score 219 · Answer 10 · 2020-11-17 18:55:09

Proof that an infinite set can be written as the countably infinite union of pairwise disjoint infinite subsets without using the axiom of choice.

score 171 · Answer 11 · 2026-03-29 20:11:32

171

Views

Prove that if every family $\mathcal{C}$ of ideals in $R$ has a maximal element then every ideal is finitely generated.

Published on 29 Mar 2026 - 20:11

score 182 · Answer 12 · 2020-11-20 21:37:52

182

Views

Axiom of choice in proof of theorem 2.41 in Rudin's principles of real analysis?

Published on 20 Nov 2020 - 21:37

score 116 · Answer 13 · 2020-11-23 14:40:01

116

Views

"Self-counting" infinite Dedekind-finite sets

Published on 23 Nov 2020 - 14:40

score 229 · Answer 14 · 2026-03-25 19:03:59

229

Views

Basis for $\mathbb{R}^\mathbb{N}$ implies axiom of choice?

Published on 25 Mar 2026 - 19:03

score 90 · Answer 15 · 2020-12-02 00:52:13

90

Views

How much choice is needed to show that $|A\times \omega|=|A|$?

Published on 02 Dec 2020 - 0:52

List Question

Does the existence of a function in this proof require the axiom of choice?

Riemann integrable function is bounded, without any type of choice

Is there a uniform way to define an upper bound on $|X|$ union of $|X|$-sized sets in ZF?

Can ZF prove the cartesian product of an ordinal by itself to be subnumerous to that ordinal?

Can $\omega_2$ be the order type of a countable union of countable sets of ordinals?

Reference Request: On the proof of $H(x)$ sets in ZF?

Does this basic cardinal inequality require the axiom of choice?

Existence of a generic filter $G$ such that $p\in G$ and Axiom of choice

If $R$ is noetherian then every family $\mathcal{C}$ of ideals in $R$ has a maximal element in $\mathcal{C}.$

Proof that an infinite set can be written as the countably infinite union of pairwise disjoint infinite subsets without using the axiom of choice.

Prove that if every family $\mathcal{C}$ of ideals in $R$ has a maximal element then every ideal is finitely generated.

Axiom of choice in proof of theorem 2.41 in Rudin's principles of real analysis?

"Self-counting" infinite Dedekind-finite sets

Basis for $\mathbb{R}^\mathbb{N}$ implies axiom of choice?

How much choice is needed to show that $|A\times \omega|=|A|$?

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