Question

How is definition of axiom of choice involving indexed family equivalent to the definition involving cartesian product?

score 65 · Answer 1 · 2020-06-19 15:40:27

65

Views

How is definition of axiom of choice involving indexed family equivalent to the definition involving cartesian product?

Published on 19 Jun 2020 - 15:40

score 186 · Answer 2 · 2026-03-30 20:57:08

186

Views

Axiom of Choice in $\kappa \cdot \kappa = \kappa$

Published on 30 Mar 2026 - 20:57

score 368 · Answer 3 · 2020-06-22 12:28:50

368

Views

Existence of complementary subspace

Published on 22 Jun 2020 - 12:28

score 89 · Answer 4 · 2020-06-28 12:04:55

89

Views

AC in Countable Union of Countable Sets

Published on 28 Jun 2020 - 12:04

score 267 · Answer 5 · 2020-06-28 18:37:52

267

Views

Is this statement equivalent to AC?

Published on 28 Jun 2020 - 18:37

score 418 · Answer 6 · 2026-03-26 01:11:42

418

Views

Is Fodor's Lemma necessary for the $\omega_1$ train station puzzle?

Published on 26 Mar 2026 - 1:11

score 113 · Answer 7 · 2020-07-09 17:54:49

113

Views

Showing that there is always an unbounded $f:X \to \mathbb{R}$ if $X$ is infinite, without choice

Published on 09 Jul 2020 - 17:54

score 53 · Answer 8 · 2020-07-18 03:42:30

53

Views

Question about sequence convergent to a limit point and Axiom of (Countable) Choice

Published on 18 Jul 2020 - 3:42

score 260 · Answer 9 · 2026-03-28 11:21:46

260

Views

Do I need Axiom of Choice for ZF construction of the Natural Numbers?

Published on 28 Mar 2026 - 11:21

score 585 · Answer 10 · 2026-03-31 22:44:41

585

Views

The complexity of finiteness

Published on 31 Mar 2026 - 22:44

score 192 · Answer 11 · 2026-03-26 13:01:35

192

Views

Could the "post-forcing continuum" be a new cardinality?

Published on 26 Mar 2026 - 13:01

score 28 · Answer 12 · 2020-07-24 08:59:36

28

Views

Construction of choice function using powerset axiom: Where am I going wrong?

Published on 24 Jul 2020 - 8:59

score 49 · Answer 13 · 2026-03-31 07:05:08

49

Views

Why cardinalities inequality defined that way?

Published on 31 Mar 2026 - 7:05

score 235 · Answer 14 · 2026-03-26 13:01:51

235

Views

Comparing the cardinalities of generic $\mathbb{R}$s

Published on 26 Mar 2026 - 13:01

score 2.7k · Answer 15 · 2026-03-29 19:28:27

2.7k

Views

Prove that the axiom of choice is necessary in order to prove something else.

Published on 29 Mar 2026 - 19:28

List Question

How is definition of axiom of choice involving indexed family equivalent to the definition involving cartesian product?

Axiom of Choice in $\kappa \cdot \kappa = \kappa$

Existence of complementary subspace

AC in Countable Union of Countable Sets

Is this statement equivalent to AC?

Is Fodor's Lemma necessary for the $\omega_1$ train station puzzle?

Showing that there is always an unbounded $f:X \to \mathbb{R}$ if $X$ is infinite, without choice

Question about sequence convergent to a limit point and Axiom of (Countable) Choice

Do I need Axiom of Choice for ZF construction of the Natural Numbers?

The complexity of finiteness

Could the "post-forcing continuum" be a new cardinality?

Construction of choice function using powerset axiom: Where am I going wrong?

Why cardinalities inequality defined that way?

Comparing the cardinalities of generic $\mathbb{R}$s

Prove that the axiom of choice is necessary in order to prove something else.

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