Question

Combinatorial proof, without axiom of choice, that for any set $A$, there is no surjection from $A^2$ to $3^A$

score 296 · Answer 1 · 2026-03-28 18:17:05

296

Views

Combinatorial proof, without axiom of choice, that for any set $A$, there is no surjection from $A^2$ to $3^A$

Published on 28 Mar 2026 - 18:17

score 178 · Answer 2 · 2024-03-25 14:24:50

178

Views

Equal number of finite and infinite subsets implies amorphous

Published on 25 Mar 2024 - 14:24

score 71 · Answer 3 · 2024-03-26 20:28:57

71

Views

The negation of countable choice for reals is consistent

Published on 26 Mar 2024 - 20:28

score 65 · Answer 4 · 2024-03-30 00:19:02

65

Views

Is there a way to construct larger cardinals without choice axiom?

Published on 30 Mar 2024 - 0:19

score 207 · Answer 5 · 2015-01-03 17:49:50

207

Views

Prove that Open Sets in $\mathbb{R}$ are The Disjoint Union of Open Intervals Without the Axioms of Choice

Published on 03 Jan 2015 - 17:49

score 285 · Answer 6 · 2015-01-04 08:42:56

285

Views

Does $\aleph_0\cdot\kappa=\kappa$ for every $\kappa\ge\aleph_0$ hold in ZF?

Published on 04 Jan 2015 - 8:42

score 642 · Answer 7 · 2015-01-06 09:39:35

642

Views

General Distributive Law and Axiom of Choice

Published on 06 Jan 2015 - 9:39

score 117 · Answer 8 · 2015-01-08 15:51:01

117

Views

Do an infinite set and its double have the same cardinality?

Published on 08 Jan 2015 - 15:51

score 260 · Answer 9 · 2015-01-08 17:31:25

260

Views

Tychonoff principle iff Wellordering principle

Published on 08 Jan 2015 - 17:31

score 794 · Answer 10 · 2015-01-16 20:31:24

794

Views

Counterexample to the Hausdorff Maximal Principle

Published on 16 Jan 2015 - 20:31

score 1.9k · Answer 11 · 2015-01-21 22:46:05

1.9k

Views

Proving without Zorn's Lemma: additive group of the reals is isomorphic to the additive group of the complex numbers

Published on 21 Jan 2015 - 22:46

score 675 · Answer 12 · 2026-03-26 20:40:48

675

Views

Does $A\times A\cong B\times B$ imply $A\cong B$?

Published on 26 Mar 2026 - 20:40

score 388 · Answer 13 · 2015-01-22 21:01:49

388

Views

Injections from all ordinals into a set $X$

Published on 22 Jan 2015 - 21:01

score 208 · Answer 14 · 2026-03-29 21:57:00

208

Views

Proof that the finite product of nonempty sets is nonempty without axiom of choice from ZF

Published on 29 Mar 2026 - 21:57

score 833 · Answer 15 · 2015-01-26 17:34:48

833

Views

Is $\text{Hom}(\prod_p \Bbb Z/p\Bbb Z, \Bbb Q) = 0$ possible without choice?

Published on 26 Jan 2015 - 17:34

List Question

Combinatorial proof, without axiom of choice, that for any set $A$, there is no surjection from $A^2$ to $3^A$

Equal number of finite and infinite subsets implies amorphous

The negation of countable choice for reals is consistent

Is there a way to construct larger cardinals without choice axiom?

Prove that Open Sets in $\mathbb{R}$ are The Disjoint Union of Open Intervals Without the Axioms of Choice

Does $\aleph_0\cdot\kappa=\kappa$ for every $\kappa\ge\aleph_0$ hold in ZF?

General Distributive Law and Axiom of Choice

Do an infinite set and its double have the same cardinality?

Tychonoff principle iff Wellordering principle

Counterexample to the Hausdorff Maximal Principle

Proving without Zorn's Lemma: additive group of the reals is isomorphic to the additive group of the complex numbers

Does $A\times A\cong B\times B$ imply $A\cong B$?

Injections from all ordinals into a set $X$

Proof that the finite product of nonempty sets is nonempty without axiom of choice from ZF

Is $\text{Hom}(\prod_p \Bbb Z/p\Bbb Z, \Bbb Q) = 0$ possible without choice?

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