Question

If $X$ is strictly amorphous and $F:X\to [X]^{<\omega}$, is the set $\bigcup\{F(x)\setminus\{x\} : x\in X\}$ finite?

score 66 · Answer 1 · 2023-02-02 15:18:36

66

Views

If $X$ is strictly amorphous and $F:X\to [X]^{<\omega}$, is the set $\bigcup\{F(x)\setminus\{x\} : x\in X\}$ finite?

Published on 02 Feb 2023 - 15:18

score 67 · Answer 2 · 2023-02-09 10:30:34

67

Views

Is it possible to construct a $\sigma-$locally finite basis of $\mathbb{R}^\omega$ in the uniform topology

Published on 09 Feb 2023 - 10:30

score 53 · Answer 3 · 2023-02-13 20:07:42

53

Views

Construction of a choice function on the open subset of R²

Published on 13 Feb 2023 - 20:07

score 74 · Answer 4 · 2023-02-14 20:34:13

74

Views

Axiom of Choice Exercise

Published on 14 Feb 2023 - 20:34

score 72 · Answer 5 · 2026-03-30 09:53:48

72

Views

Parting ways with uncountable choice

Published on 30 Mar 2026 - 9:53

score 163 · Answer 6 · 2023-02-16 00:56:47

163

Views

Does $|X|^m\cdot n^{|X|}\le (n+m)^{|X|}$ hold without choice?

Published on 16 Feb 2023 - 0:56

score 631 · Answer 7 · 2026-03-27 00:04:34

631

Views

Can free groups on different cardinals be isomorphic in ZF?

Published on 27 Mar 2026 - 0:04

score 190 · Answer 8 · 2026-03-26 14:23:06

190

Views

Are constructivists in favor of the Property of Baire?

Published on 26 Mar 2026 - 14:23

score 291 · Answer 9 · 2026-04-01 16:25:00

291

Views

For infinite cardinal $\kappa$, $\kappa$ . $\kappa$ = $\kappa$ . Set Theory Enderton p-162, Lemma 6R

Published on 01 Apr 2026 - 16:25

score 217 · Answer 10 · 2026-03-25 19:05:42

217

Views

Is Hahn-Banach equivalent to the ultrafilter lemma in ZF

Published on 25 Mar 2026 - 19:05

score 56 · Answer 11 · 2023-03-02 03:12:57

In ZF the following holds: if there is an injection from $\omega$ to $\mathcal{P}(X)$, then there is a surjection from $X$ to $\omega$.

score 113 · Answer 12 · 2023-03-03 18:30:32

113

Views

Is there a name for this choice principle?

Published on 03 Mar 2023 - 18:30

score 65 · Answer 13 · 2023-03-04 12:36:28

65

Views

Using Zorn's Lemma, for a function $f: X \to Y$, show that the poset of partial sections of $f$, $((A, u), ≤)$, is non-empty.

Published on 04 Mar 2023 - 12:36

score 55 · Answer 14 · 2026-03-26 08:14:31

55

Views

Simple Zorn Lemma application doubt.

Published on 26 Mar 2026 - 8:14

score 36 · Answer 15 · 2023-03-17 05:34:59

36

Views

Question about rational functions of the 'variables' in an arbitrary set $X$

Published on 17 Mar 2023 - 5:34

List Question

If $X$ is strictly amorphous and $F:X\to [X]^{<\omega}$, is the set $\bigcup\{F(x)\setminus\{x\} : x\in X\}$ finite?

Is it possible to construct a $\sigma-$locally finite basis of $\mathbb{R}^\omega$ in the uniform topology

Construction of a choice function on the open subset of R²

Axiom of Choice Exercise

Parting ways with uncountable choice

Does $|X|^m\cdot n^{|X|}\le (n+m)^{|X|}$ hold without choice?

Can free groups on different cardinals be isomorphic in ZF?

Are constructivists in favor of the Property of Baire?

For infinite cardinal $\kappa$, $\kappa$ . $\kappa$ = $\kappa$ . Set Theory Enderton p-162, Lemma 6R

Is Hahn-Banach equivalent to the ultrafilter lemma in ZF

In ZF the following holds: if there is an injection from $\omega$ to $\mathcal{P}(X)$, then there is a surjection from $X$ to $\omega$.

Is there a name for this choice principle?

Using Zorn's Lemma, for a function $f: X \to Y$, show that the poset of partial sections of $f$, $((A, u), ≤)$, is non-empty.

Simple Zorn Lemma application doubt.

Question about rational functions of the 'variables' in an arbitrary set $X$

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