Question

Intuitionistic Banach-Tarski Paradox

score 1.1k · Answer 1 · 2012-07-27 00:17:25

1.1k

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Intuitionistic Banach-Tarski Paradox

Published on 27 Jul 2012 - 0:17

score 543 · Answer 2 · 2012-07-29 11:13:39

543

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Stronger than ZF, weaker than ZFC

Published on 29 Jul 2012 - 11:13

score 1.1k · Answer 3 · 2012-07-29 22:26:27

1.1k

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Heine-Borel Theorem ($\mathbb{R}^k$) (in ZF)

Published on 29 Jul 2012 - 22:26

score 555 · Answer 4 · 2012-07-30 10:25:26

555

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True Statement in ZF is true statement in ZFC?

Published on 30 Jul 2012 - 10:25

score 1.1k · Answer 5 · 2012-07-30 18:02:46

1.1k

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(ZF) Every nonempty perfect set in $\mathbb{R}^k$ is uncountable.

Published on 30 Jul 2012 - 18:02

score 5.1k · Answer 6 · 2012-07-30 21:06:54

5.1k

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Is there a Cantor-Schroder-Bernstein statement about surjective maps?

Published on 30 Jul 2012 - 21:06

score 186 · Answer 7 · 2012-08-01 16:36:04

186

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Does the Cartesian product get smaller if I use fewer sets?

Published on 01 Aug 2012 - 16:36

score 2.2k · Answer 8 · 2012-08-03 00:06:45

2.2k

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Proving that the set of algebraic numbers is countable without AC

Published on 03 Aug 2012 - 0:06

score 1.3k · Answer 9 · 2012-08-04 10:55:40

1.3k

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Is a countable product of compact intervals in $\mathbf R$ compact (without using the AC)?

Published on 04 Aug 2012 - 10:55

score 226 · Answer 10 · 2012-08-06 08:57:01

226

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Showing the bijection between countable dense subset of a metric space $E×\mathbb{Q}→$neighborhoods of $E$ with rational radius

Published on 06 Aug 2012 - 8:57

score 2.8k · Answer 11 · 2012-08-06 17:41:57

2.8k

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some elementary questions about cardinality

Published on 06 Aug 2012 - 17:41

score 720 · Answer 12 · 2012-08-08 10:21:56

720

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If every infinite subset has a limit point in a metric space $X$, then $X$ is separable (in ZF)

Published on 08 Aug 2012 - 10:21

score 137 · Answer 13 · 2012-08-09 09:05:29

137

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(ZF) Dedekind infinite + Limit Point Compact ⇒ Separable

Published on 09 Aug 2012 - 9:05

score 1.4k · Answer 14 · 2012-08-10 07:16:20

1.4k

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Is cardinality a total order? Is AC necessary?

Published on 10 Aug 2012 - 7:16

score 299 · Answer 15 · 2012-08-10 08:53:08

299

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Sum of cardinals without AC

Published on 10 Aug 2012 - 8:53

List Question

Intuitionistic Banach-Tarski Paradox

Stronger than ZF, weaker than ZFC

Heine-Borel Theorem ($\mathbb{R}^k$) (in ZF)

True Statement in ZF is true statement in ZFC?

(ZF) Every nonempty perfect set in $\mathbb{R}^k$ is uncountable.

Is there a Cantor-Schroder-Bernstein statement about surjective maps?

Does the Cartesian product get smaller if I use fewer sets?

Proving that the set of algebraic numbers is countable without AC

Is a countable product of compact intervals in $\mathbf R$ compact (without using the AC)?

Showing the bijection between countable dense subset of a metric space $E×\mathbb{Q}→$neighborhoods of $E$ with rational radius

some elementary questions about cardinality

If every infinite subset has a limit point in a metric space $X$, then $X$ is separable (in ZF)

(ZF) Dedekind infinite + Limit Point Compact ⇒ Separable

Is cardinality a total order? Is AC necessary?

Sum of cardinals without AC

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