Question

Which sequences arise as the eventuality filter of a sequence?

score 71 · Answer 1 · 2026-04-29 12:29:00

71

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Which sequences arise as the eventuality filter of a sequence?

Published on 29 Apr 2026 - 12:29

score 205 · Answer 2 · 2026-04-29 12:28:44

205

Views

The proof of Generic Model Theorem (14.5) in Jech's Set Theory p.218

Published on 29 Apr 2026 - 12:28

score 114 · Answer 3 · 2026-05-07 10:07:22

114

Views

Possibility of preserving the ultrafilter on $\mathcal{P}_{\kappa}(\lambda)$ in V[G] after forcing with a <$\kappa$ directed closed poset?

Published on 07 May 2026 - 10:07

score 385 · Answer 4 · 2026-05-07 13:54:01

385

Views

Any filter is contained in a ultrafilter - Proof Explanation

Published on 07 May 2026 - 13:54

score 105 · Answer 5 · 2026-04-29 12:29:01

105

Views

Can two filters be "separated"?

Published on 29 Apr 2026 - 12:29

score 113 · Answer 6 · 2026-04-29 12:28:59

113

Views

Bijection between filters and ideals

Published on 29 Apr 2026 - 12:28

score 111 · Answer 7 · 2026-04-29 12:28:58

111

Views

Fill gaps in a topology proof

Published on 29 Apr 2026 - 12:28

score 443 · Answer 8 · 2026-05-02 23:51:37

443

Views

If $\mathcal{F}$ is a filter on a set $X$, then there exists an ultrafilter $\mathcal{U}$ such that $\mathcal{F} \subseteq \mathcal{U}$

Published on 02 May 2026 - 23:51

score 302 · Answer 9 · 2026-05-07 17:02:07

302

Views

Let $X$ be a finite set. Prove that every ultrafilter is a point filter.

Published on 07 May 2026 - 17:02

score 133 · Answer 10 · 2026-04-29 12:29:01

133

Views

Filters and surjectivity of functions

Published on 29 Apr 2026 - 12:29

score 49 · Answer 11 · 2026-05-02 18:30:14

49

Views

Two filters which converge to the same point are equivalent modulo $R$

Published on 02 May 2026 - 18:30

score 103 · Answer 12 · 2026-04-29 12:55:26

103

Views

Equivalent filters converge to the same point

Published on 29 Apr 2026 - 12:55

score 45 · Answer 13 · 2026-04-29 12:55:12

45

Views

Filter generates a topology compatible with the vector structure of $X$.

Published on 29 Apr 2026 - 12:55

score 312 · Answer 14 · 2026-04-29 12:55:02

312

Views

Non-principal filter of $\mathcal P(\mathbb N)$ cannot contain singleton

Published on 29 Apr 2026 - 12:55

score 134 · Answer 15 · 2026-04-29 12:55:18

134

Views

If $\mathbb{P}\in M$ is atomless and the filter $G$ is $\mathbb{P}$-generic over M, then $G\not\in M$.

Published on 29 Apr 2026 - 12:55

List Question

Which sequences arise as the eventuality filter of a sequence?

The proof of Generic Model Theorem (14.5) in Jech's Set Theory p.218

Possibility of preserving the ultrafilter on $\mathcal{P}_{\kappa}(\lambda)$ in V[G] after forcing with a <$\kappa$ directed closed poset?

Any filter is contained in a ultrafilter - Proof Explanation

Can two filters be "separated"?

Bijection between filters and ideals

Fill gaps in a topology proof

If $\mathcal{F}$ is a filter on a set $X$, then there exists an ultrafilter $\mathcal{U}$ such that $\mathcal{F} \subseteq \mathcal{U}$

Let $X$ be a finite set. Prove that every ultrafilter is a point filter.

Filters and surjectivity of functions

Two filters which converge to the same point are equivalent modulo $R$

Equivalent filters converge to the same point

Filter generates a topology compatible with the vector structure of $X$.

Non-principal filter of $\mathcal P(\mathbb N)$ cannot contain singleton

If $\mathbb{P}\in M$ is atomless and the filter $G$ is $\mathbb{P}$-generic over M, then $G\not\in M$.

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