Question

If a set $S$ has a choice function, does $\bigcup S$ have one too?

score 223 · Answer 1 · 2015-07-06 13:07:51

223

Views

If a set $S$ has a choice function, does $\bigcup S$ have one too?

Published on 06 Jul 2015 - 13:07

score 1.9k · Answer 2 · 2015-07-09 13:43:08

1.9k

Views

W. Mückenheim claims a severe inconsistency of transfinite set theory; true?

Published on 09 Jul 2015 - 13:43

score 893 · Answer 3 · 2015-07-12 20:51:34

893

Views

Where is the axiom of choice used in Rudin's proof of "the countable union of countable sets is countable"?

Published on 12 Jul 2015 - 20:51

score 626 · Answer 4 · 2015-07-14 03:53:38

626

Views

Does this proposition from complex analysis depend on AC?

Published on 14 Jul 2015 - 3:53

score 65 · Answer 5 · 2015-07-15 09:13:23

65

Views

Find a uniquely defined element in this $\aleph_1$-indexed Cartesian product

Published on 15 Jul 2015 - 9:13

score 1.1k · Answer 6 · 2015-07-15 17:12:50

1.1k

Views

Prob. 9, Sec. 4.3, in Kreyszig's Functional Analysis Book: Proof of the Hahn Banach Theorem without Zorn's Lemma

Published on 15 Jul 2015 - 17:12

score 1k · Answer 7 · 2015-07-20 09:28:09

1k

Views

Does Lowenheim-Skolem theorem depend on axiom of choice?

Published on 20 Jul 2015 - 9:28

score 448 · Answer 8 · 2015-07-27 12:46:52

448

Views

Explicit construction of a nonmeasurable set, where only the proof of correctness uses choice?

Published on 27 Jul 2015 - 12:46

score 118 · Answer 9 · 2026-03-28 08:08:45

118

Views

Approximating nice functions with wild ones

Published on 28 Mar 2026 - 8:08

score 290 · Answer 10 · 2015-08-01 18:55:05

290

Views

Does construction of infinite product measure require axiom of choice?

Published on 01 Aug 2015 - 18:55

score 117 · Answer 11 · 2015-08-02 21:11:48

117

Views

Over ZF does "every non-seperable Hilbert space has an orthonormal basis" imply "there exists a non-Lebesgue measurable set"?

Published on 02 Aug 2015 - 21:11

score 78 · Answer 12 · 2015-08-03 17:51:22

78

Views

Can it be proved without the axiom of choice that every cardinal is comparable with every finite cardinal?

Published on 03 Aug 2015 - 17:51

score 976 · Answer 13 · 2015-08-03 18:21:11

976

Views

Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?

Published on 03 Aug 2015 - 18:21

score 258 · Answer 14 · 2015-08-06 18:50:43

258

Views

Topological properties of $[0,\omega_1)$ without choice.

Published on 06 Aug 2015 - 18:50

score 782 · Answer 15 · 2026-03-27 16:17:31

782

Views

Is there a turing machine for which halting is equivalent to the Axiom of Choice or its negation?

Published on 27 Mar 2026 - 16:17

List Question

If a set $S$ has a choice function, does $\bigcup S$ have one too?

W. Mückenheim claims a severe inconsistency of transfinite set theory; true?

Where is the axiom of choice used in Rudin's proof of "the countable union of countable sets is countable"?

Does this proposition from complex analysis depend on AC?

Find a uniquely defined element in this $\aleph_1$-indexed Cartesian product

Prob. 9, Sec. 4.3, in Kreyszig's Functional Analysis Book: Proof of the Hahn Banach Theorem without Zorn's Lemma

Does Lowenheim-Skolem theorem depend on axiom of choice?

Explicit construction of a nonmeasurable set, where only the proof of correctness uses choice?

Approximating nice functions with wild ones

Does construction of infinite product measure require axiom of choice?

Over ZF does "every non-seperable Hilbert space has an orthonormal basis" imply "there exists a non-Lebesgue measurable set"?

Can it be proved without the axiom of choice that every cardinal is comparable with every finite cardinal?

Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?

Topological properties of $[0,\omega_1)$ without choice.

Is there a turing machine for which halting is equivalent to the Axiom of Choice or its negation?

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