Question

Is the Axiom of Choice needed for a Vitali set of algebraic numbers?

score 649 · Answer 1 · 2026-02-23 01:23:49

649

Views

Is the Axiom of Choice needed for a Vitali set of algebraic numbers?

Published on 23 Feb 2026 - 1:23

score 1k · Answer 2 · 2026-03-26 06:15:12

1k

Views

Where does this proof of the Continuum Hypothesis use the axiom of choice?

Published on 26 Mar 2026 - 6:15

score 100 · Answer 3 · 2018-07-09 10:56:54

100

Views

Proof verification: Assuming choice, if $A$ is infinite then $|A|\geq\aleph_{0}$

Published on 09 Jul 2018 - 10:56

score 56 · Answer 4 · 2018-07-09 16:12:49

56

Views

Proving Variants of the Axiom of Choice

Published on 09 Jul 2018 - 16:12

score 185 · Answer 5 · 2018-07-09 23:30:41

185

Views

Does the proof of rank-nullity theorem from Lang's "Linear Algebra" involves axiom of choice?

Published on 09 Jul 2018 - 23:30

score 311 · Answer 6 · 2026-03-25 03:01:04

311

Views

Is countable choice enough to prove that there are continuum-many Borel sets?

Published on 25 Mar 2026 - 3:01

score 102 · Answer 7 · 2018-07-11 07:52:22

102

Views

Proving "For an infinite set $X$, if $X=A\uplus B$ then $|X|=|A|$ or $|X|=|B|$" is equivalent to the axiom of choice

Published on 11 Jul 2018 - 7:52

score 278 · Answer 8 · 2018-07-15 07:29:51

278

Views

Without axiom of choice

Published on 15 Jul 2018 - 7:29

score 819 · Answer 9 · 2026-03-25 08:12:42

819

Views

How do we define functions on quotient sets?

Published on 25 Mar 2026 - 8:12

score 271 · Answer 10 · 2026-03-25 16:02:31

271

Views

the power set of every well-ordered set is well-ordered implies well ordering

Published on 25 Mar 2026 - 16:02

score 33 · Answer 11 · 2026-03-27 21:36:22

33

Views

Does every iterative definition (or at least the one describe in the details) require the use of the Axiom of Choice?

Published on 27 Mar 2026 - 21:36

score 353 · Answer 12 · 2018-08-03 17:08:28

353

Views

algebraic geometry for specific fields means no axiom of choice?

Published on 03 Aug 2018 - 17:08

score 74 · Answer 13 · 2026-03-26 01:10:18

74

Views

Non-continuous additive map without AC(Axiom of choice)

Published on 26 Mar 2026 - 1:10

score 85 · Answer 14 · 2018-08-07 20:28:16

85

Views

Set theory - Solution without using the Axiom of Choice.

Published on 07 Aug 2018 - 20:28

score 121 · Answer 15 · 2026-03-29 03:52:56

121

Views

Compact spaces that depend on choice?

Published on 29 Mar 2026 - 3:52

List Question

Is the Axiom of Choice needed for a Vitali set of algebraic numbers?

Where does this proof of the Continuum Hypothesis use the axiom of choice?

Proof verification: Assuming choice, if $A$ is infinite then $|A|\geq\aleph_{0}$

Proving Variants of the Axiom of Choice

Does the proof of rank-nullity theorem from Lang's "Linear Algebra" involves axiom of choice?

Is countable choice enough to prove that there are continuum-many Borel sets?

Proving "For an infinite set $X$, if $X=A\uplus B$ then $|X|=|A|$ or $|X|=|B|$" is equivalent to the axiom of choice

Without axiom of choice

How do we define functions on quotient sets?

the power set of every well-ordered set is well-ordered implies well ordering

Does every iterative definition (or at least the one describe in the details) require the use of the Axiom of Choice?

algebraic geometry for specific fields means no axiom of choice?

Non-continuous additive map without AC(Axiom of choice)

Set theory - Solution without using the Axiom of Choice.

Compact spaces that depend on choice?

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