Question

Define non-eventually-constant $f: I \to \{a, b\}$ from arbitrary upwards-directed poset $I$

score 82 · Answer 1 · 2026-05-10 14:05:53

82

Views

Define non-eventually-constant $f: I \to \{a, b\}$ from arbitrary upwards-directed poset $I$

Published on 10 May 2026 - 14:05

score 357 · Answer 2 · 2026-04-13 04:46:54

357

Views

Not $\sigma$-compact set without axiom of choice

Published on 13 Apr 2026 - 4:46

score 433 · Answer 3 · 2026-05-11 04:39:48

433

Views

Partition of positive reals with each part closed under addition without choice

Published on 11 May 2026 - 4:39

score 121 · Answer 4 · 2026-04-11 07:24:55

121

Views

is it consistent with AC that every set is measurable?

Published on 11 Apr 2026 - 7:24

score 75 · Answer 5 · 2026-04-14 05:55:06

75

Views

℩-descriptor and the axiom of choice?

Published on 14 Apr 2026 - 5:55

score 609 · Answer 6 · 2026-04-13 03:38:54

609

Views

Sequential compactness $\rightarrow$ limit point compactness and axiom of choice

Published on 13 Apr 2026 - 3:38

score 213 · Answer 7 · 2026-04-15 00:12:09

213

Views

Linear order of the quotient generated from Vitali relation implies non-measurability of subset of reals

Published on 15 Apr 2026 - 0:12

score 408 · Answer 8 · 2026-04-14 00:19:39

408

Views

Existence of complement of a subspace without Zorn's lemma

Published on 14 Apr 2026 - 0:19

score 792 · Answer 9 · 2026-04-16 12:54:51

792

Views

Example of a set of real numbers that is Dedekind-finite but not finite

Published on 16 Apr 2026 - 12:54

score 874 · Answer 10 · 2026-04-10 17:37:13

874

Views

How to solve this puzzle by using Axiom of Choice?

Published on 10 Apr 2026 - 17:37

score 97 · Answer 11 · 2026-04-14 02:14:10

97

Views

Possible use of choice in proving "Compactness implies limit point compactness"

Published on 14 Apr 2026 - 2:14

score 187 · Answer 12 · 2026-05-10 19:48:59

187

Views

Is real analysis constructive?

Published on 10 May 2026 - 19:48

score 128 · Answer 13 · 2026-04-14 03:51:07

128

Views

Avoiding choice in proving "Sequential compactness implies Lebesgue Number Lemma"

Published on 14 Apr 2026 - 3:51

score 102 · Answer 14 · 2026-04-11 08:41:31

102

Views

Is there a notion that quantify the dependence of a proof on AC?

Published on 11 Apr 2026 - 8:41

score 108 · Answer 15 · 2026-04-12 01:57:38

108

Views

Why do we need axiom of choice to prove that there does not a exist definition of $P(A)$, defined for all subsets $A \subset [0, 1]$

Published on 12 Apr 2026 - 1:57

List Question

Define non-eventually-constant $f: I \to \{a, b\}$ from arbitrary upwards-directed poset $I$

Not $\sigma$-compact set without axiom of choice

Partition of positive reals with each part closed under addition without choice

is it consistent with AC that every set is measurable?

℩-descriptor and the axiom of choice?

Sequential compactness $\rightarrow$ limit point compactness and axiom of choice

Linear order of the quotient generated from Vitali relation implies non-measurability of subset of reals

Existence of complement of a subspace without Zorn's lemma

Example of a set of real numbers that is Dedekind-finite but not finite

How to solve this puzzle by using Axiom of Choice?

Possible use of choice in proving "Compactness implies limit point compactness"

Is real analysis constructive?

Avoiding choice in proving "Sequential compactness implies Lebesgue Number Lemma"

Is there a notion that quantify the dependence of a proof on AC?

Why do we need axiom of choice to prove that there does not a exist definition of $P(A)$, defined for all subsets $A \subset [0, 1]$

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