Question

How can we show that the intersection of a series of closed unbounded sets is closed unbounded?

score 381 · Answer 1 · 2026-04-14 22:07:39

381

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How can we show that the intersection of a series of closed unbounded sets is closed unbounded?

Published on 14 Apr 2026 - 22:07

score 69 · Answer 2 · 2026-04-15 03:18:34

69

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Is every limit cardinal $\alpha$ of the form $\alpha=card(X)+card(P(X))+cardP(P(X))+...$, for some set $X$?

Published on 15 Apr 2026 - 3:18

score 112 · Answer 3 · 2026-04-16 07:32:32

The relation between the limit cardinal $\alpha$ and a sequence of cardinal numbers strictly less than $\alpha$

score 119 · Answer 4 · 2026-04-12 10:50:11

119

Views

Finite chain condition - Variation of Martin's Axiom statement

Published on 12 Apr 2026 - 10:50

score 71 · Answer 5 · 2026-04-15 19:13:16

Let $α$ and $β$ be ordinals such that $α>1$ and $β\neq0$. Let $γ$, $ζ$, and $η$ be ordinals st $γ<β$, $ζ<α$, and $η<α^{γ}$. Prove $α^γ ζ+η<α^{β}$.

score 163 · Answer 6 · 2026-04-12 08:34:35

163

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Proof of the Solovay Theorem in Jech

Published on 12 Apr 2026 - 8:34

score 792 · Answer 7 · 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 84 · Answer 8 · 2026-04-09 10:05:12

84

Views

How is this definition of closedness compatible with the order topology?

Published on 09 Apr 2026 - 10:05

score 108 · Answer 9 · 2026-04-13 01:21:24

Is there any "reasonable" definition of cardinality which agrees with the standard definition on finite sets but disagrees on infinite sets?

score 386 · Answer 10 · 2026-04-09 11:40:08

386

Views

What features of a logic make possible the proof of Downward Lowenheim-Skolem?

Published on 09 Apr 2026 - 11:40

score 266 · Answer 11 · 2026-04-11 00:16:51

266

Views

Question about the proof of the Recursion Theorem

Published on 11 Apr 2026 - 0:16

score 177 · Answer 12 · 2026-04-11 09:57:49

177

Views

Constant functions in set-theory

Published on 11 Apr 2026 - 9:57

score 57 · Answer 13 · 2026-04-14 13:40:13

57

Views

Prove that (if $R$ is set-like, then its transitive closure is set-like) implies the axiom of replacement

Published on 14 Apr 2026 - 13:40

score 38 · Answer 14 · 2026-04-13 12:27:05

38

Views

restricted 3- space can be a field?

Published on 13 Apr 2026 - 12:27

score 77 · Answer 15 · 2026-04-16 07:11:23

77

Views

Equivalent condition for a cardinal number to be of cofinality $\aleph_0$

Published on 16 Apr 2026 - 7:11

List Question

How can we show that the intersection of a series of closed unbounded sets is closed unbounded?

Is every limit cardinal $\alpha$ of the form $\alpha=card(X)+card(P(X))+cardP(P(X))+...$, for some set $X$?

The relation between the limit cardinal $\alpha$ and a sequence of cardinal numbers strictly less than $\alpha$

Finite chain condition - Variation of Martin's Axiom statement

Let $α$ and $β$ be ordinals such that $α>1$ and $β\neq0$. Let $γ$, $ζ$, and $η$ be ordinals st $γ<β$, $ζ<α$, and $η<α^{γ}$. Prove $α^γ ζ+η<α^{β}$.

Proof of the Solovay Theorem in Jech

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

How is this definition of closedness compatible with the order topology?

Is there any "reasonable" definition of cardinality which agrees with the standard definition on finite sets but disagrees on infinite sets?

What features of a logic make possible the proof of Downward Lowenheim-Skolem?

Question about the proof of the Recursion Theorem

Constant functions in set-theory

Prove that (if $R$ is set-like, then its transitive closure is set-like) implies the axiom of replacement

restricted 3- space can be a field?

Equivalent condition for a cardinal number to be of cofinality $\aleph_0$

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