Question

If the quotientspace $=^+$ is linearly orderable then why has the graph $Z$ chromatic number $2$?

score 49 · Answer 1 · 2021-05-20 10:26:33

49

Views

If the quotientspace $=^+$ is linearly orderable then why has the graph $Z$ chromatic number $2$?

Published on 20 May 2021 - 10:26

score 66 · Answer 2 · 2021-05-20 16:42:03

66

Views

Opposite Schröder-Cantor-Bernstein to show that there is an injection from $\mathbb{N}$ to any infinite set $X$.

Published on 20 May 2021 - 16:42

score 120 · Answer 3 · 2021-05-21 18:38:27

120

Views

A question about equivalence of well-foundedness notions and if they beg a form of choice?

Published on 21 May 2021 - 18:38

score 168 · Answer 4 · 2026-03-28 06:17:46

168

Views

How far are WO and AC equivalent?

Published on 28 Mar 2026 - 6:17

score 104 · Answer 5 · 2021-05-29 09:42:31

Why do we need axiom of choice to prove that if $f\colon A\to B$ is surjective, then there is $C\subseteq A$ such that $C$ and $B$ are equipotent?

score 91 · Answer 6 · 2021-06-03 00:17:16

91

Views

If $|A| > |B|$, then $|A-B| > |B-A|$?

Published on 03 Jun 2021 - 0:17

score 151 · Answer 7 · 2021-06-07 20:43:02

151

Views

Prove $A\approx A\times A$ using Zorn's Lemma

Published on 07 Jun 2021 - 20:43

score 91 · Answer 8 · 2021-06-09 14:37:31

91

Views

Can we say that any Dedekind-finite family of sets has a choice function without AC?

Published on 09 Jun 2021 - 14:37

score 142 · Answer 9 · 2021-06-17 16:32:55

142

Views

Family of pairwise distinct elements

Published on 17 Jun 2021 - 16:32

score 74 · Answer 10 · 2026-04-07 18:24:22

74

Views

Do tree choice lead to set choice?

Published on 07 Apr 2026 - 18:24

score 80 · Answer 11 · 2021-06-20 09:23:44

80

Views

Proof of Axiom of Choice $\Rightarrow$ Zorn's Lemma: How is AC applied?

Published on 20 Jun 2021 - 9:23

score 332 · Answer 12 · 2021-06-22 02:02:34

332

Views

What is an example of model of ZF with a countable family of pairs whose union is uncountable?

Published on 22 Jun 2021 - 2:02

score 39 · Answer 13 · 2026-04-06 15:06:23

39

Views

Finding surjections from some subsets of $\omega^2$ to $\omega$ many at most countable ordinals without choice.

Published on 06 Apr 2026 - 15:06

score 122 · Answer 14 · 2021-06-23 19:25:49

122

Views

Reading on permutation models

Published on 23 Jun 2021 - 19:25

score 184 · Answer 15 · 2021-06-25 07:50:07

184

Views

Cardinality of cartesian product and axiom of choice

Published on 25 Jun 2021 - 7:50

List Question

If the quotientspace $=^+$ is linearly orderable then why has the graph $Z$ chromatic number $2$?

Opposite Schröder-Cantor-Bernstein to show that there is an injection from $\mathbb{N}$ to any infinite set $X$.

A question about equivalence of well-foundedness notions and if they beg a form of choice?

How far are WO and AC equivalent?

Why do we need axiom of choice to prove that if $f\colon A\to B$ is surjective, then there is $C\subseteq A$ such that $C$ and $B$ are equipotent?

If $|A| > |B|$, then $|A-B| > |B-A|$?

Prove $A\approx A\times A$ using Zorn's Lemma

Can we say that any Dedekind-finite family of sets has a choice function without AC?

Family of pairwise distinct elements

Do tree choice lead to set choice?

Proof of Axiom of Choice $\Rightarrow$ Zorn's Lemma: How is AC applied?

What is an example of model of ZF with a countable family of pairs whose union is uncountable?

Finding surjections from some subsets of $\omega^2$ to $\omega$ many at most countable ordinals without choice.

Reading on permutation models

Cardinality of cartesian product and axiom of choice

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