Question

Is the Axiom of Choice needed in this kind of reasoning?

score 143 · Answer 1 · 2021-10-15 17:55:16

143

Views

Is the Axiom of Choice needed in this kind of reasoning?

Published on 15 Oct 2021 - 17:55

score 243 · Answer 2 · 2026-04-04 03:55:32

243

Views

Connection between the many different definitions of the Axiom of Choice

Published on 04 Apr 2026 - 3:55

score 84 · Answer 3 · 2021-10-21 19:55:33

84

Views

Can you construct a Vitali set under ZF?

Published on 21 Oct 2021 - 19:55

score 254 · Answer 4 · 2021-10-24 20:34:39

254

Views

Proving that $\mathbb{Q}$ is an injective abelian group without the Axiom of Choice

Published on 24 Oct 2021 - 20:34

score 39 · Answer 5 · 2021-10-31 01:31:35

39

Views

Why doesn't family of finite nonempty sets have choice function?

Published on 31 Oct 2021 - 1:31

score 388 · Answer 6 · 2026-03-25 15:44:10

388

Views

Why must we use Zorn's Lemma to prove every subgroup of $G$ is contained in a maximal subgroup of $G$?

Published on 25 Mar 2026 - 15:44

score 104 · Answer 7 · 2026-03-29 02:31:21

104

Views

Well-ordering $\mathbb R$ in ZF + "$2^{\aleph_0} \nrightarrow (\aleph_1, \aleph_1)^2$".

Published on 29 Mar 2026 - 2:31

score 33 · Answer 8 · 2021-11-07 18:22:56

33

Views

Reference request for proof that there is no non-trivial translation invariant measure on the power set of $\Bbb R^n$ which does not invoke AC

Published on 07 Nov 2021 - 18:22

score 80 · Answer 9 · 2021-11-08 04:37:02

80

Views

Is size N (infinite) union of countable sets at most as big as N?

Published on 08 Nov 2021 - 4:37

score 42 · Answer 10 · 2021-11-09 06:31:53

Is $B_x = c\circ f(x)$ in the proof of Lemma 13.1 on p.80 in "Topology 2nd Edition" by James R. Munkres? (Question about choice function)

score 194 · Answer 11 · 2026-03-28 03:55:26

194

Views

How is the axiom of choice used (or not used) in the proof of the Lesbegue covering theorem in Andrej Bauer's paper in constructive mathematics?

Published on 28 Mar 2026 - 3:55

score 178 · Answer 12 · 2021-11-10 21:08:04

178

Views

In ZF, can a Dedekind-finite set (or even an amorphous set) be smaller than a non-trivial partition of its elements?

Published on 10 Nov 2021 - 21:08

score 101 · Answer 13 · 2026-04-06 18:45:13

101

Views

Finding a winning strategy for a game in ZF + “$\omega_1$ is regular”.

Published on 06 Apr 2026 - 18:45

score 72 · Answer 14 · 2021-11-12 20:52:38

72

Views

Proving that choice holds in $V_{\alpha}$ for all $\alpha$

Published on 12 Nov 2021 - 20:52

score 73 · Answer 15 · 2021-11-13 08:48:25

Is it possible to define a function for every point in its domain such that every point maps to its family of open balls without the axiom of choice?

List Question

Is the Axiom of Choice needed in this kind of reasoning?

Connection between the many different definitions of the Axiom of Choice

Can you construct a Vitali set under ZF?

Proving that $\mathbb{Q}$ is an injective abelian group without the Axiom of Choice

Why doesn't family of finite nonempty sets have choice function?

Why must we use Zorn's Lemma to prove every subgroup of $G$ is contained in a maximal subgroup of $G$?

Well-ordering $\mathbb R$ in ZF + "$2^{\aleph_0} \nrightarrow (\aleph_1, \aleph_1)^2$".

Reference request for proof that there is no non-trivial translation invariant measure on the power set of $\Bbb R^n$ which does not invoke AC

Is size N (infinite) union of countable sets at most as big as N?

Is $B_x = c\circ f(x)$ in the proof of Lemma 13.1 on p.80 in "Topology 2nd Edition" by James R. Munkres? (Question about choice function)

How is the axiom of choice used (or not used) in the proof of the Lesbegue covering theorem in Andrej Bauer's paper in constructive mathematics?

In ZF, can a Dedekind-finite set (or even an amorphous set) be smaller than a non-trivial partition of its elements?

Finding a winning strategy for a game in ZF + “$\omega_1$ is regular”.

Proving that choice holds in $V_{\alpha}$ for all $\alpha$

Is it possible to define a function for every point in its domain such that every point maps to its family of open balls without the axiom of choice?

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