Question

Are there any purely semantic proofs of the compactness theorem that don't use the full axiom of choice?

score 286 · Answer 1 · 2026-04-13 02:04:19

286

Views

Are there any purely semantic proofs of the compactness theorem that don't use the full axiom of choice?

Published on 13 Apr 2026 - 2:04

score 162 · Answer 2 · 2026-04-10 03:42:43

162

Views

Are ACF and Ultrafilter Lemma/BPIT equivalent?

Published on 10 Apr 2026 - 3:42

score 136 · Answer 3 · 2026-04-10 06:01:41

136

Views

Is this proof legal?

Published on 10 Apr 2026 - 6:01

score 725 · Answer 4 · 2026-04-11 18:38:22

725

Views

Partial order on cardinalities without the axiom of choice

Published on 11 Apr 2026 - 18:38

score 317 · Answer 5 · 2026-04-16 15:54:09

317

Views

Proof that $\mathbb{N}\times \mathbb{N}\cong \mathbb{N}$ without $AC_\omega$ or Arithmetic

Published on 16 Apr 2026 - 15:54

score 318 · Answer 6 · 2026-04-13 23:36:06

318

Views

Confusion Regarding the Axiom of Countable Choice

Published on 13 Apr 2026 - 23:36

score 115 · Answer 7 · 2026-04-12 10:02:02

115

Views

Application of the axiom of choice

Published on 12 Apr 2026 - 10:02

score 485 · Answer 8 · 2026-04-15 17:08:43

485

Views

Theorem 4.15 page 22, Real and Abstract Analysis, Hewitt and Stromberg

Published on 15 Apr 2026 - 17:08

score 147 · Answer 9 · 2026-04-12 15:21:45

147

Views

Choosing elements of linear orders

Published on 12 Apr 2026 - 15:21

score 321 · Answer 10 · 2026-04-10 21:22:19

321

Views

What is the role of induction in the proof of König's Lemma?

Published on 10 Apr 2026 - 21:22

score 193 · Answer 11 · 2026-04-14 22:01:32

193

Views

Proving Equivalence of Two Version of Axiom of Choice

Published on 14 Apr 2026 - 22:01

score 3.1k · Answer 12 · 2026-04-12 08:29:44

3.1k

Views

Do we need Axiom of Choice to make infinite choices from a set?

Published on 12 Apr 2026 - 8:29

score 436 · Answer 13 · 2026-04-11 20:18:15

436

Views

Does Vitali set imply the axiom of choice

Published on 11 Apr 2026 - 20:18

score 166 · Answer 14 · 2026-04-15 15:43:22

166

Views

Bernstein sets, Well-Ordering theorem vs Axiom of Choice

Published on 15 Apr 2026 - 15:43

score 306 · Answer 15 · 2026-04-14 04:44:56

306

Views

Can we prove without the axiom of choice that subspaces of finite dimensional vector spaces are finite dimensional as well?

Published on 14 Apr 2026 - 4:44

List Question

Are there any purely semantic proofs of the compactness theorem that don't use the full axiom of choice?

Are ACF and Ultrafilter Lemma/BPIT equivalent?

Is this proof legal?

Partial order on cardinalities without the axiom of choice

Proof that $\mathbb{N}\times \mathbb{N}\cong \mathbb{N}$ without $AC_\omega$ or Arithmetic

Confusion Regarding the Axiom of Countable Choice

Application of the axiom of choice

Theorem 4.15 page 22, Real and Abstract Analysis, Hewitt and Stromberg

Choosing elements of linear orders

What is the role of induction in the proof of König's Lemma?

Proving Equivalence of Two Version of Axiom of Choice

Do we need Axiom of Choice to make infinite choices from a set?

Does Vitali set imply the axiom of choice

Bernstein sets, Well-Ordering theorem vs Axiom of Choice

Can we prove without the axiom of choice that subspaces of finite dimensional vector spaces are finite dimensional as well?

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