Question

Proving that these facts are equivalent: 1. $cf(\alpha)>\kappa$ 2. $\forall X\subseteq V_\alpha \;\; |X|\leq\kappa \;\; X\in V_\alpha$

score 48 · Answer 1 · 2026-03-28 10:29:16

48

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Proving that these facts are equivalent: 1. $cf(\alpha)>\kappa$ 2. $\forall X\subseteq V_\alpha \;\; |X|\leq\kappa \;\; X\in V_\alpha$

Published on 28 Mar 2026 - 10:29

score 372 · Answer 2 · 2020-07-10 08:54:58

372

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Prove that the powerset of a finite set is finite. (correct proof or abuse of definitions?)

Published on 10 Jul 2020 - 8:54

score 98 · Answer 3 · 2026-03-28 10:29:15

98

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Prove that $|V_\alpha|=|\operatorname{P}(\alpha)|$ if and only if $\alpha=\{2,\omega+1\}$ or $\alpha=\kappa+1$, $\kappa=\beth_\kappa$

Published on 28 Mar 2026 - 10:29

score 32 · Answer 4 · 2020-07-10 21:15:37

Prove that $A\setminus B$ is non-countable where $A$ is a non-countable set and $B\subseteq A$ is a countable set.

score 239 · Answer 5 · 2020-07-11 10:27:24

239

Views

Proving that there exists an uncountable number of distinct basis of the euclidean topology on $\mathbb R$

Published on 11 Jul 2020 - 10:27

score 33 · Answer 6 · 2020-07-11 16:33:27

33

Views

Simple cardinal arithmetic

Published on 11 Jul 2020 - 16:33

score 55 · Answer 7 · 2020-07-20 14:16:50

55

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A question about cardinality

Published on 20 Jul 2020 - 14:16

score 71 · Answer 8 · 2020-07-21 14:13:23

71

Views

Question on cardinality of a set

Published on 21 Jul 2020 - 14:13

score 163 · Answer 9 · 2026-03-26 01:28:45

163

Views

Example of Separable Product Space with cardinality greater than continuum?

Published on 26 Mar 2026 - 1:28

score 26 · Answer 10 · 2020-07-25 10:48:01

26

Views

Question about relating cardinalities

Published on 25 Jul 2020 - 10:48

score 48 · Answer 11 · 2020-07-25 17:35:05

48

Views

Why cardinalities inequality defined that way?

Published on 25 Jul 2020 - 17:35

score 265 · Answer 12 · 2020-07-29 07:27:50

265

Views

On cardinality of varieties (Hartshorne I.4.8, following Hartshorne's hint)

Published on 29 Jul 2020 - 7:27

score 54 · Answer 13 · 2020-07-30 10:22:41

54

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Infinite number of variables and infinite number of equations

Published on 30 Jul 2020 - 10:22

score 154 · Answer 14 · 2020-07-30 10:51:02

154

Views

Cardinality of double cosets

Published on 30 Jul 2020 - 10:51

score 152 · Answer 15 · 2020-07-31 07:13:37

152

Views

Proving $2^m \not\leq m^2$ for infinite cardinal $m$ without AC

Published on 31 Jul 2020 - 7:13

List Question

Proving that these facts are equivalent: 1. $cf(\alpha)>\kappa$ 2. $\forall X\subseteq V_\alpha \;\; |X|\leq\kappa \;\; X\in V_\alpha$

Prove that the powerset of a finite set is finite. (correct proof or abuse of definitions?)

Prove that $|V_\alpha|=|\operatorname{P}(\alpha)|$ if and only if $\alpha=\{2,\omega+1\}$ or $\alpha=\kappa+1$, $\kappa=\beth_\kappa$

Prove that $A\setminus B$ is non-countable where $A$ is a non-countable set and $B\subseteq A$ is a countable set.

Proving that there exists an uncountable number of distinct basis of the euclidean topology on $\mathbb R$

Simple cardinal arithmetic

A question about cardinality

Question on cardinality of a set

Example of Separable Product Space with cardinality greater than continuum?

Question about relating cardinalities

Why cardinalities inequality defined that way?

On cardinality of varieties (Hartshorne I.4.8, following Hartshorne's hint)

Infinite number of variables and infinite number of equations

Cardinality of double cosets

Proving $2^m \not\leq m^2$ for infinite cardinal $m$ without AC

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