Question

The Ultrafilter Principle as a midway between Axiom of Choice and the Axiom of Choice for Finite Sets?

score 146 · Answer 1 · 2026-04-10 19:29:30

146

Views

The Ultrafilter Principle as a midway between Axiom of Choice and the Axiom of Choice for Finite Sets?

Published on 10 Apr 2026 - 19:29

score 216 · Answer 2 · 2026-05-11 05:07:58

216

Views

Ultrafilter principle and Axiom of Dependent Choice as 'nonconstructive and constructive' components of the Axiom of Choice

Published on 11 May 2026 - 5:07

score 180 · Answer 3 · 2026-04-13 22:10:57

180

Views

If the Power Set of $S$ is an infinite Dedekind-finite set, what can be concluded about $S$?

Published on 13 Apr 2026 - 22:10

score 108 · Answer 4 · 2026-04-14 00:31:07

108

Views

Ultrafilter Principle + Hausdorffness as a substitute of the Axiom of Choice

Published on 14 Apr 2026 - 0:31

score 75 · Answer 5 · 2026-04-11 23:13:56

75

Views

Is group homomorphism $F: SO(3) \to \mathbb R-\{0\}$ unique?

Published on 11 Apr 2026 - 23:13

score 99 · Answer 6 · 2026-04-14 14:27:46

99

Views

Existence of A Linear Right Inverse Between Finite Dimensional Vector Spaces

Published on 14 Apr 2026 - 14:27

score 180 · Answer 7 · 2026-04-08 05:30:33

180

Views

Axiom of Choice as a tool for proving measurability

Published on 08 Apr 2026 - 5:30

score 104 · Answer 8 · 2026-04-14 14:33:17

104

Views

Axiom of Choice for finite vs infinite product of sets

Published on 14 Apr 2026 - 14:33

score 66 · Answer 9 · 2026-04-13 10:56:18

66

Views

List of theorems equivalent to choice

Published on 13 Apr 2026 - 10:56

score 117 · Answer 10 · 2026-04-10 17:35:04

117

Views

Difficulty understanding Axiom of Choice

Published on 10 Apr 2026 - 17:35

score 60 · Answer 11 · 2026-04-13 21:49:33

60

Views

Let $X,Y$ be metric spaces. Then a function $f:X \to Y$ is continuous at $x$ if and only if $f$ is sequentially continuous at $x$

Published on 13 Apr 2026 - 21:49

score 112 · Answer 12 · 2026-04-17 12:37:47

112

Views

Transversal duality for upwards-closed subsets of ${\cal P}(X)$

Published on 17 Apr 2026 - 12:37

score 101 · Answer 13 · 2026-04-11 21:35:45

101

Views

What’s ‘Function’ in Axiom of Choice?

Published on 11 Apr 2026 - 21:35

score 181 · Answer 14 · 2026-04-11 23:47:24

181

Views

How to decide the cardinality of $\{\text{all group isomorphisms from }(\mathbb{R},+)\text{ onto }(\mathbb{R}^+,\cdot)\}$?

Published on 11 Apr 2026 - 23:47

score 365 · Answer 15 · 2026-04-12 05:40:24

365

Views

Can the set of endomorphisms of $(\mathbb{R},+)$ have cardinality strictly between $\mathfrak c^ c$ and $\frak c $?

Published on 12 Apr 2026 - 5:40

List Question

The Ultrafilter Principle as a midway between Axiom of Choice and the Axiom of Choice for Finite Sets?

Ultrafilter principle and Axiom of Dependent Choice as 'nonconstructive and constructive' components of the Axiom of Choice

If the Power Set of $S$ is an infinite Dedekind-finite set, what can be concluded about $S$?

Ultrafilter Principle + Hausdorffness as a substitute of the Axiom of Choice

Is group homomorphism $F: SO(3) \to \mathbb R-\{0\}$ unique?

Existence of A Linear Right Inverse Between Finite Dimensional Vector Spaces

Axiom of Choice as a tool for proving measurability

Axiom of Choice for finite vs infinite product of sets

List of theorems equivalent to choice

Difficulty understanding Axiom of Choice

Let $X,Y$ be metric spaces. Then a function $f:X \to Y$ is continuous at $x$ if and only if $f$ is sequentially continuous at $x$

Transversal duality for upwards-closed subsets of ${\cal P}(X)$

What’s ‘Function’ in Axiom of Choice?

How to decide the cardinality of $\{\text{all group isomorphisms from }(\mathbb{R},+)\text{ onto }(\mathbb{R}^+,\cdot)\}$?

Can the set of endomorphisms of $(\mathbb{R},+)$ have cardinality strictly between $\mathfrak c^ c$ and $\frak c $?

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