Question

Can't we choose any particular element from $^{A}B$ without the axiom of choice?

score 147 · Answer 1 · 2022-02-15 04:24:14

147

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Can't we choose any particular element from $^{A}B$ without the axiom of choice?

Published on 15 Feb 2022 - 4:24

score 349 · Answer 2 · 2022-02-18 23:11:31

349

Views

Proving without the Axiom of Choice (A.C.) that increasing real functions have countable discontinuities

Published on 18 Feb 2022 - 23:11

score 96 · Answer 3 · 2022-02-21 03:08:36

96

Views

Every chain of subsets of $\mathbb{N}$ has a countable subchain with equal intersection

Published on 21 Feb 2022 - 3:08

score 64 · Answer 4 · 2022-02-23 19:31:43

64

Views

Function $f: \omega \to A$ with $f(0)=a$ and $f(i)Rf(i+1)$ in ZF

Published on 23 Feb 2022 - 19:31

score 32 · Answer 5 · 2022-03-01 12:32:30

32

Views

Non-measurable sets construction

Published on 01 Mar 2022 - 12:32

score 161 · Answer 6 · 2022-03-01 18:26:03

161

Views

Goldrei "Classic Set Theory" Exercise $5.11$

Published on 01 Mar 2022 - 18:26

score 272 · Answer 7 · 2022-03-08 22:48:01

272

Views

Proving that a set is dedekind-infinite if and only if it has a countably infinite subset

Published on 08 Mar 2022 - 22:48

score 104 · Answer 8 · 2022-03-15 12:21:20

104

Views

Suppose $a$ is small and $F: a \rightarrow b$ is a surjection. Is $b$ small?

Published on 15 Mar 2022 - 12:21

score 174 · Answer 9 · 2026-03-28 11:32:13

174

Views

Does ZF prove that the union of a $\subseteq$-chain of well-orderable sets is again well-orderable?

Published on 28 Mar 2026 - 11:32

score 53 · Answer 10 · 2022-03-24 21:00:56

53

Views

How does the set of choice functions look like while proving the axiom of choice from ZF+Zorn’s lemma

Published on 24 Mar 2022 - 21:00

score 54 · Answer 11 · 2022-03-26 16:39:58

54

Views

Connected subset of $\mathbb{R}^2$ with disconnected sections

Published on 26 Mar 2022 - 16:39

score 57 · Answer 12 · 2026-03-29 19:11:46

57

Views

Without the axiom of choice, is there always a partition refining a collection of sets that is the same size?

Published on 29 Mar 2026 - 19:11

score 108 · Answer 13 · 2022-04-01 08:13:47

108

Views

Example of surjective function without right-inverse (without AoC)

Published on 01 Apr 2022 - 8:13

score 139 · Answer 14 · 2022-04-01 08:43:28

139

Views

Does every proof that abelian groups are amenable rely on the axiom of choice?

Published on 01 Apr 2022 - 8:43

score 83 · Answer 15 · 2022-04-06 23:22:17

83

Views

Finite Unions of Equinumerous Sets

Published on 06 Apr 2022 - 23:22

List Question

Can't we choose any particular element from $^{A}B$ without the axiom of choice?

Proving without the Axiom of Choice (A.C.) that increasing real functions have countable discontinuities

Every chain of subsets of $\mathbb{N}$ has a countable subchain with equal intersection

Function $f: \omega \to A$ with $f(0)=a$ and $f(i)Rf(i+1)$ in ZF

Non-measurable sets construction

Goldrei "Classic Set Theory" Exercise $5.11$

Proving that a set is dedekind-infinite if and only if it has a countably infinite subset

Suppose $a$ is small and $F: a \rightarrow b$ is a surjection. Is $b$ small?

Does ZF prove that the union of a $\subseteq$-chain of well-orderable sets is again well-orderable?

How does the set of choice functions look like while proving the axiom of choice from ZF+Zorn’s lemma

Connected subset of $\mathbb{R}^2$ with disconnected sections

Without the axiom of choice, is there always a partition refining a collection of sets that is the same size?

Example of surjective function without right-inverse (without AoC)

Does every proof that abelian groups are amenable rely on the axiom of choice?

Finite Unions of Equinumerous Sets

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