Question

First Uncountable Ordinal Cofinality: Needs AC?

score 392 · Answer 1 · 2026-03-30 10:54:44

392

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First Uncountable Ordinal Cofinality: Needs AC?

Published on 30 Mar 2026 - 10:54

score 626 · Answer 2 · 2015-06-17 14:40:29

626

Views

Proof that every field $F$ has an algebraic closure $\bar F$

Published on 17 Jun 2015 - 14:40

score 1.1k · Answer 3 · 2015-06-18 01:49:29

"Sequential continuity is equivalent to $\epsilon$-$\delta $ continuity " implies Axiom of countable choice for collection of subsets of $\mathbb R$?

score 214 · Answer 4 · 2015-06-18 01:57:52

214

Views

Does there exist a model of $ZF¬C$ in which there is a function on $\mathbb R$ which is sequentially continuous at a point where it is not continuous?

Published on 18 Jun 2015 - 1:57

score 398 · Answer 5 · 2015-06-23 03:42:43

398

Views

Are there weak versions of the axiom of choice equivalent to weak versions of Zorn's lemma and similar principles?

Published on 23 Jun 2015 - 3:42

score 321 · Answer 6 · 2015-06-24 13:08:37

321

Views

Does the principle of schematic dependent choice follow from ZFCU?

Published on 24 Jun 2015 - 13:08

score 187 · Answer 7 · 2015-06-25 04:15:25

187

Views

dual Dedekind-infinity may not imply Dedekind-infinite without AC

Published on 25 Jun 2015 - 4:15

score 40 · Answer 8 · 2015-06-26 05:39:43

40

Views

The least $\aleph$ that has no surjective map from $m$ to it.

Published on 26 Jun 2015 - 5:39

score 133 · Answer 9 · 2015-06-26 21:43:42

133

Views

Basis for $\mathbb{R}^{\infty}$

Published on 26 Jun 2015 - 21:43

score 303 · Answer 10 · 2015-06-27 07:28:44

303

Views

A Banach space of (Hamel) dimension $\kappa$ exists if and only if $\kappa^{\aleph_0}=\kappa$

Published on 27 Jun 2015 - 7:28

score 281 · Answer 11 · 2015-06-26 21:58:28

281

Views

What is the significance of having Prime Ideal Theorem in models for failure of Axiom of Choice?

Published on 26 Jun 2015 - 21:58

score 718 · Answer 12 · 2026-03-27 22:11:36

718

Views

Good resources for studying independence proofs

Published on 27 Mar 2026 - 22:11

score 500 · Answer 13 · 2026-03-30 11:04:54

500

Views

Does the definition of the fundamental group implicitly assume the Axiom of Choice?

Published on 30 Mar 2026 - 11:04

score 1.2k · Answer 14 · 2015-07-02 19:05:42

1.2k

Views

Transitive Closure of a Well-Founded Relation is Well-Founded (without Axiom of Choice)

Published on 02 Jul 2015 - 19:05

score 63 · Answer 15 · 2015-07-06 11:20:44

63

Views

If $n < \aleph^*(m)$, then $n < 2^m$.

Published on 06 Jul 2015 - 11:20

List Question

First Uncountable Ordinal Cofinality: Needs AC?

Proof that every field $F$ has an algebraic closure $\bar F$

"Sequential continuity is equivalent to $\epsilon$-$\delta $ continuity " implies Axiom of countable choice for collection of subsets of $\mathbb R$?

Does there exist a model of $ZF¬C$ in which there is a function on $\mathbb R$ which is sequentially continuous at a point where it is not continuous?

Are there weak versions of the axiom of choice equivalent to weak versions of Zorn's lemma and similar principles?

Does the principle of schematic dependent choice follow from ZFCU?

dual Dedekind-infinity may not imply Dedekind-infinite without AC

The least $\aleph$ that has no surjective map from $m$ to it.

Basis for $\mathbb{R}^{\infty}$

A Banach space of (Hamel) dimension $\kappa$ exists if and only if $\kappa^{\aleph_0}=\kappa$

What is the significance of having Prime Ideal Theorem in models for failure of Axiom of Choice?

Good resources for studying independence proofs

Does the definition of the fundamental group implicitly assume the Axiom of Choice?

Transitive Closure of a Well-Founded Relation is Well-Founded (without Axiom of Choice)

If $n < \aleph^*(m)$, then $n < 2^m$.

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