Question

How can I prove that every infinite set has a countably infinite subset using only the Axiom of Countable Choice?

score 231 · Answer 1 · 2020-04-20 08:39:53

231

Views

How can I prove that every infinite set has a countably infinite subset using only the Axiom of Countable Choice?

Published on 20 Apr 2020 - 8:39

score 30 · Answer 2 · 2020-04-20 11:37:44

30

Views

Strange applications of the Axiom of Choice

Published on 20 Apr 2020 - 11:37

score 99 · Answer 3 · 2020-04-21 22:04:48

99

Views

Bypassing the axiom of choice when there are infinitely many sets but there are constraints on the sets

Published on 21 Apr 2020 - 22:04

score 41 · Answer 4 · 2020-04-22 15:29:54

41

Views

Am I using the axiom of choice in the measure-theory proof?

Published on 22 Apr 2020 - 15:29

score 529 · Answer 5 · 2026-03-26 11:01:09

529

Views

There is a $\Sigma^1_1$ universal set and this is not Borel. Where did we use the axiom of choice?

Published on 26 Mar 2026 - 11:01

score 157 · Answer 6 · 2026-03-30 10:33:31

157

Views

If $x$ is a set of cardinality $\kappa$ and $\lambda<\kappa$, do we need the axiom of choice to prove that there is a subset of $x$ of size $\lambda$?

Published on 30 Mar 2026 - 10:33

score 134 · Answer 7 · 2026-03-25 19:51:38

134

Views

Are finite projective modules locally free without axiom of choice?

Published on 25 Mar 2026 - 19:51

score 86 · Answer 8 · 2026-03-26 04:35:02

86

Views

Axiom of Choice and fullness of the class of terms of the forcing language

Published on 26 Mar 2026 - 4:35

score 63 · Answer 9 · 2020-04-28 10:07:06

63

Views

If there exists a surjection $f:A\to B$, can you construct an injection $f:B\to P(A)$?

Published on 28 Apr 2020 - 10:07

score 182 · Answer 10 · 2020-04-29 08:40:42

182

Views

How much choice follows from the existence of derangement?

Published on 29 Apr 2020 - 8:40

score 106 · Answer 11 · 2026-03-25 07:44:52

106

Views

How much choice is needed to prove that every compact metric space is a continuous image of the Cantor set?

Published on 25 Mar 2026 - 7:44

score 146 · Answer 12 · 2020-05-03 12:45:38

146

Views

Dependent choice and $L(\mathbb R)$.

Published on 03 May 2020 - 12:45

score 133 · Answer 13 · 2020-05-07 01:07:46

133

Views

Not Assuming Choice, Nilradical Not Equal to Intersection of Prime Ideals

Published on 07 May 2020 - 1:07

score 90 · Answer 14 · 2026-03-25 01:18:44

90

Views

On Axiom of Choice and the principle of Explosion (ex contradictione sequitur quodlibet)

Published on 25 Mar 2026 - 1:18

score 47 · Answer 15 · 2020-05-07 20:44:11

47

Views

What is the strength of a stationary costationary subset of $\omega_1$?

Published on 07 May 2020 - 20:44

List Question

How can I prove that every infinite set has a countably infinite subset using only the Axiom of Countable Choice?

Strange applications of the Axiom of Choice

Bypassing the axiom of choice when there are infinitely many sets but there are constraints on the sets

Am I using the axiom of choice in the measure-theory proof?

There is a $\Sigma^1_1$ universal set and this is not Borel. Where did we use the axiom of choice?

If $x$ is a set of cardinality $\kappa$ and $\lambda<\kappa$, do we need the axiom of choice to prove that there is a subset of $x$ of size $\lambda$?

Are finite projective modules locally free without axiom of choice?

Axiom of Choice and fullness of the class of terms of the forcing language

If there exists a surjection $f:A\to B$, can you construct an injection $f:B\to P(A)$?

How much choice follows from the existence of derangement?

How much choice is needed to prove that every compact metric space is a continuous image of the Cantor set?

Dependent choice and $L(\mathbb R)$.

Not Assuming Choice, Nilradical Not Equal to Intersection of Prime Ideals

On Axiom of Choice and the principle of Explosion (ex contradictione sequitur quodlibet)

What is the strength of a stationary costationary subset of $\omega_1$?

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