Question

Does proving that surjective linear transformation has a right inverse require Axiom of Choice?

score 806 · Answer 1 · 2017-09-16 10:09:56

806

Views

Does proving that surjective linear transformation has a right inverse require Axiom of Choice?

Published on 16 Sep 2017 - 10:09

score 457 · Answer 2 · 2017-09-16 18:43:06

457

Views

Construction of amorphous subset of $\Bbb R$

Published on 16 Sep 2017 - 18:43

score 421 · Answer 3 · 2026-04-01 23:14:40

421

Views

How did the axiom of choice become the boogeyman?

Published on 01 Apr 2026 - 23:14

score 303 · Answer 4 · 2017-09-18 13:55:43

303

Views

Is usage of axiom of countable choice unavoidable to prove this?

Published on 18 Sep 2017 - 13:55

score 1.6k · Answer 5 · 2017-09-19 00:17:45

1.6k

Views

Russell's shoes and socks

Published on 19 Sep 2017 - 0:17

score 90 · Answer 6 · 2026-03-26 16:10:17

90

Views

What are examples of the use of countable choice axiom and DC in (pseudo)riemannian geometry results

Published on 26 Mar 2026 - 16:10

score 78 · Answer 7 · 2017-09-21 09:33:01

78

Views

countable union of countable families of countable sets is a countable family

Published on 21 Sep 2017 - 9:33

score 107 · Answer 8 · 2017-09-21 19:28:50

107

Views

Cardinality of set of finite subsets of $A$ equals cardinality of $A$

Published on 21 Sep 2017 - 19:28

score 99 · Answer 9 · 2017-09-22 01:32:18

99

Views

Group structure and the axiom of choice

Published on 22 Sep 2017 - 1:32

score 72 · Answer 10 · 2017-09-23 14:11:41

72

Views

Number theoretic statement which follows from ZF+AC, and whose negation follows from ZF+$\neg$AC

Published on 23 Sep 2017 - 14:11

score 145 · Answer 11 · 2017-09-24 03:25:23

145

Views

Are there non-intuitive consequences of the ultrafilter lemma?

Published on 24 Sep 2017 - 3:25

score 89 · Answer 12 · 2026-03-28 19:39:48

89

Views

Necessity and correctness of Haussdorf's maximal principle in $5B$ covering lemma proof

Published on 28 Mar 2026 - 19:39

score 178 · Answer 13 · 2017-09-25 05:03:26

178

Views

On axiom of choice

Published on 25 Sep 2017 - 5:03

score 437 · Answer 14 · 2017-09-26 16:54:35

437

Views

If $T$ is one-to-one linear transformation, then can we prove that $T$ has a left inverse transformation without AC?

Published on 26 Sep 2017 - 16:54

score 111 · Answer 15 · 2017-09-29 01:11:29

111

Views

Error in a proof that union of a countable number of at most countable sets is at most countable

Published on 29 Sep 2017 - 1:11

List Question

Does proving that surjective linear transformation has a right inverse require Axiom of Choice?

Construction of amorphous subset of $\Bbb R$

How did the axiom of choice become the boogeyman?

Is usage of axiom of countable choice unavoidable to prove this?

Russell's shoes and socks

What are examples of the use of countable choice axiom and DC in (pseudo)riemannian geometry results

countable union of countable families of countable sets is a countable family

Cardinality of set of finite subsets of $A$ equals cardinality of $A$

Group structure and the axiom of choice

Number theoretic statement which follows from ZF+AC, and whose negation follows from ZF+$\neg$AC

Are there non-intuitive consequences of the ultrafilter lemma?

Necessity and correctness of Haussdorf's maximal principle in $5B$ covering lemma proof

On axiom of choice

If $T$ is one-to-one linear transformation, then can we prove that $T$ has a left inverse transformation without AC?

Error in a proof that union of a countable number of at most countable sets is at most countable

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