Question

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

score 652 · Answer 1 · 2026-05-10 19:23:33

652

Views

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

Published on 10 May 2026 - 19:23

score 1k · Answer 2 · 2026-05-10 19:21:43

1k

Views

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

Published on 10 May 2026 - 19:21

score 105 · Answer 3 · 2026-05-10 19:21:49

105

Views

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

Published on 10 May 2026 - 19:21

score 60 · Answer 4 · 2026-05-10 19:21:12

60

Views

Proving Variants of the Axiom of Choice

Published on 10 May 2026 - 19:21

score 190 · Answer 5 · 2026-05-10 19:21:41

190

Views

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

Published on 10 May 2026 - 19:21

score 315 · Answer 6 · 2026-05-10 19:21:20

315

Views

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

Published on 10 May 2026 - 19:21

score 106 · Answer 7 · 2026-05-10 19:21:12

106

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 10 May 2026 - 19:21

score 286 · Answer 8 · 2026-05-10 21:11:58

286

Views

Without axiom of choice

Published on 10 May 2026 - 21:11

score 822 · Answer 9 · 2026-05-11 06:50:14

822

Views

How do we define functions on quotient sets?

Published on 11 May 2026 - 6:50

score 275 · Answer 10 · 2026-05-10 19:21:12

275

Views

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

Published on 10 May 2026 - 19:21

score 36 · Answer 11 · 2026-05-10 19:21:20

36

Views

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

Published on 10 May 2026 - 19:21

score 360 · Answer 12 · 2026-05-10 19:21:50

360

Views

algebraic geometry for specific fields means no axiom of choice?

Published on 10 May 2026 - 19:21

score 77 · Answer 13 · 2026-05-10 19:21:21

77

Views

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

Published on 10 May 2026 - 19:21

score 89 · Answer 14 · 2026-05-10 19:21:20

89

Views

Set theory - Solution without using the Axiom of Choice.

Published on 10 May 2026 - 19:21

score 125 · Answer 15 · 2026-05-10 19:21:42

125

Views

Compact spaces that depend on choice?

Published on 10 May 2026 - 19:21

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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