Question

If every partitioning of $X$ has a choice function, is $X$ necessarily well-orderable?

score 86 · Answer 1 · 2016-04-01 16:28:32

86

Views

If every partitioning of $X$ has a choice function, is $X$ necessarily well-orderable?

Published on 01 Apr 2016 - 16:28

score 112 · Answer 2 · 2026-03-31 09:23:04

112

Views

Choice function without AC in special case

Published on 31 Mar 2026 - 9:23

score 138 · Answer 3 · 2016-04-02 06:41:53

138

Views

Uncountable dense sets of reals without the axiom of choice

Published on 02 Apr 2016 - 6:41

score 1.8k · Answer 4 · 2016-04-04 11:01:11

1.8k

Views

Why can't Axiom of Choice be proven by Rule C

Published on 04 Apr 2016 - 11:01

score 583 · Answer 5 · 2026-04-01 00:57:02

583

Views

Is the axiom of induction constructively verifiable for a non-standard model of arithmetic?

Published on 01 Apr 2026 - 0:57

score 226 · Answer 6 · 2016-04-13 03:12:05

226

Views

Does $\operatorname{card}(X) < \operatorname{card}(Y)$ imply $\operatorname{card}(X^2) < \operatorname{card}(Y^2)$ without choice?

Published on 13 Apr 2016 - 3:12

score 320 · Answer 7 · 2016-04-15 13:23:06

320

Views

Hausdorff Maximal Principle

Published on 15 Apr 2016 - 13:23

score 405 · Answer 8 · 2026-03-26 01:21:42

405

Views

Proving Hahn-Banach theorem directly

Published on 26 Mar 2026 - 1:21

score 53 · Answer 9 · 2026-03-31 07:56:46

53

Views

Hyperplanes without Axiom of Choice

Published on 31 Mar 2026 - 7:56

score 65 · Answer 10 · 2026-03-29 10:49:04

65

Views

Does the relationship between Jonsson Cardinals and Jonsson Algebras require the axiom of choice?

Published on 29 Mar 2026 - 10:49

score 526 · Answer 11 · 2016-04-17 19:35:45

526

Views

Is the equivalence of the ascending chain condition and the maximum condition equivalent to the axiom of dependent choice?

Published on 17 Apr 2016 - 19:35

score 154 · Answer 12 · 2016-04-19 01:08:28

154

Views

Does König's inequality require axiom of choice?

Published on 19 Apr 2016 - 1:08

score 188 · Answer 13 · 2016-04-21 06:38:51

188

Views

Comparability of a set and a subset of power set.

Published on 21 Apr 2016 - 6:38

score 282 · Answer 14 · 2016-04-21 14:05:01

282

Views

Without the Axiom of Choice, $\aleph_0<2^{\aleph_0}$ implies $\aleph_1\le 2^{\aleph_0}$?

Published on 21 Apr 2016 - 14:05

score 64 · Answer 15 · 2016-04-24 20:05:23

64

Views

Regarding Choice in fields outside set theory.

Published on 24 Apr 2016 - 20:05

List Question

If every partitioning of $X$ has a choice function, is $X$ necessarily well-orderable?

Choice function without AC in special case

Uncountable dense sets of reals without the axiom of choice

Why can't Axiom of Choice be proven by Rule C

Is the axiom of induction constructively verifiable for a non-standard model of arithmetic?

Does $\operatorname{card}(X) < \operatorname{card}(Y)$ imply $\operatorname{card}(X^2) < \operatorname{card}(Y^2)$ without choice?

Hausdorff Maximal Principle

Proving Hahn-Banach theorem directly

Hyperplanes without Axiom of Choice

Does the relationship between Jonsson Cardinals and Jonsson Algebras require the axiom of choice?

Is the equivalence of the ascending chain condition and the maximum condition equivalent to the axiom of dependent choice?

Does König's inequality require axiom of choice?

Comparability of a set and a subset of power set.

Without the Axiom of Choice, $\aleph_0<2^{\aleph_0}$ implies $\aleph_1\le 2^{\aleph_0}$?

Regarding Choice in fields outside set theory.

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