Question

Partitions of the Cantor space into parities

score 170 · Answer 1 · 2026-04-11 10:01:32

170

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Partitions of the Cantor space into parities

Published on 11 Apr 2026 - 10:01

score 169 · Answer 2 · 2026-04-15 16:46:16

169

Views

Could induction give us an infinite sequence of sets $X_1 \subseteq X_2 \subseteq \cdots$ or do we need the axiom of choice?

Published on 15 Apr 2026 - 16:46

score 42 · Answer 3 · 2026-04-11 19:03:55

42

Views

Is the Axiom of Choice restricted to $\Bbb R$ independent of ZF?

Published on 11 Apr 2026 - 19:03

score 357 · Answer 4 · 2026-04-09 07:32:40

357

Views

infinite Cartesian products

Published on 09 Apr 2026 - 7:32

score 344 · Answer 5 · 2026-04-13 02:45:23

344

Views

Why do we need the axiom of choice in showing the non-emptiness of an infinite Cartesian product

Published on 13 Apr 2026 - 2:45

score 590 · Answer 6 · 2026-04-10 00:03:01

590

Views

Is the Axiom of Choice necessary to prove $\mathbb R \approx \mathcal P(\omega)$?

Published on 10 Apr 2026 - 0:03

score 735 · Answer 7 · 2026-04-10 19:37:00

735

Views

How do we get a simplicial homology functor?

Published on 10 Apr 2026 - 19:37

score 396 · Answer 8 · 2026-05-11 09:33:39

396

Views

An explicit construction for an everywhere discontinuous real function with $F((a+b)/2)\leq(F(a)+F(b))/2$?

Published on 11 May 2026 - 9:33

score 205 · Answer 9 · 2026-04-09 13:33:18

205

Views

Examples of figures whose area depend on axiom of choice

Published on 09 Apr 2026 - 13:33

score 1.5k · Answer 10 · 2026-04-14 10:46:30

1.5k

Views

Proof of: $X$ is finite $\iff X$ is Tarski-finite

Published on 14 Apr 2026 - 10:46

score 890 · Answer 11 · 2026-05-11 06:19:32

890

Views

What is the definition of the Feferman-Levy model?

Published on 11 May 2026 - 6:19

score 41 · Answer 12 · 2026-04-11 01:11:31

41

Views

Writing the ZF formula for the choice function (given Well-ordering)

Published on 11 Apr 2026 - 1:11

score 468 · Answer 13 · 2026-04-08 17:10:05

468

Views

Is "PA has no non-standard models" consistent with ZF?

Published on 08 Apr 2026 - 17:10

score 349 · Answer 14 · 2026-04-15 12:20:05

349

Views

Proof of "Every vector space has a basis $\implies$ AC" without mentioning von Neumann hierarchy

Published on 15 Apr 2026 - 12:20

score 289 · Answer 15 · 2026-04-12 19:32:09

289

Views

Characterization of dense open subsets of the real numbers

Published on 12 Apr 2026 - 19:32

List Question

Partitions of the Cantor space into parities

Could induction give us an infinite sequence of sets $X_1 \subseteq X_2 \subseteq \cdots$ or do we need the axiom of choice?

Is the Axiom of Choice restricted to $\Bbb R$ independent of ZF?

infinite Cartesian products

Why do we need the axiom of choice in showing the non-emptiness of an infinite Cartesian product

Is the Axiom of Choice necessary to prove $\mathbb R \approx \mathcal P(\omega)$?

How do we get a simplicial homology functor?

An explicit construction for an everywhere discontinuous real function with $F((a+b)/2)\leq(F(a)+F(b))/2$?

Examples of figures whose area depend on axiom of choice

Proof of: $X$ is finite $\iff X$ is Tarski-finite

What is the definition of the Feferman-Levy model?

Writing the ZF formula for the choice function (given Well-ordering)

Is "PA has no non-standard models" consistent with ZF?

Proof of "Every vector space has a basis $\implies$ AC" without mentioning von Neumann hierarchy

Characterization of dense open subsets of the real numbers

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