Question

finite sequences,linear order, lexicographic order, well order, cardinal

score 423 · Answer 1 · 2015-02-04 15:07:17

423

Views

finite sequences,linear order, lexicographic order, well order, cardinal

Published on 04 Feb 2015 - 15:07

score 89 · Answer 2 · 2015-02-04 19:48:24

89

Views

Is $f: \mathcal{P}(\omega) \to \omega \cup \lbrace \omega \rbrace, \ x \mapsto \bigcup \lbrace n \in \omega: n \subset x \rbrace $ surjective?

Published on 04 Feb 2015 - 19:48

score 376 · Answer 3 · 2015-02-08 12:20:33

376

Views

Lexicographic order on $\alpha^\beta$ is well-ordered

Published on 08 Feb 2015 - 12:20

score 433 · Answer 4 · 2015-02-08 18:42:37

433

Views

How do we know that $\omega_1$ exists in ZF?

Published on 08 Feb 2015 - 18:42

score 319 · Answer 5 · 2015-02-13 11:01:49

319

Views

Does every countable sequence of ordinals converge?

Published on 13 Feb 2015 - 11:01

score 65 · Answer 6 · 2015-02-13 20:49:11

65

Views

A question about well-ordered subsets of partially ordered sets

Published on 13 Feb 2015 - 20:49

score 252 · Answer 7 · 2015-02-14 23:47:47

252

Views

Ordinals that are not cardinals

Published on 14 Feb 2015 - 23:47

score 102 · Answer 8 · 2026-03-26 07:52:43

102

Views

If $f\colon\kappa\rightarrow\kappa$, then the set of all $\alpha < \kappa$ such that $f(\xi) < \alpha$ for all $\xi < \alpha$ is closed and unbounded.

Published on 26 Mar 2026 - 7:52

score 93 · Answer 9 · 2015-02-15 12:49:28

93

Views

What is wrong with the following function $f:ON \rightarrow ON$?

Published on 15 Feb 2015 - 12:49

score 38 · Answer 10 · 2015-02-15 14:28:04

38

Views

Given stationary set $A$ of $k$, there exists an ordinals $\alpha$ such that $A$ contains all limit ordinals greater then $\alpha$

Published on 15 Feb 2015 - 14:28

score 71 · Answer 11 · 2015-02-16 00:55:51

71

Views

Do ordinal sets exist?

Published on 16 Feb 2015 - 0:55

score 181 · Answer 12 · 2026-03-25 13:55:32

181

Views

Theorem $($Transfinite Induction and Construction$)$ (James Dugundji - 5.1, Page - 40)

Published on 25 Mar 2026 - 13:55

score 335 · Answer 13 · 2015-02-24 17:18:40

335

Views

How to prove $cf(\aleph_{\omega_1})=\omega_1$?

Published on 24 Feb 2015 - 17:18

score 134 · Answer 14 · 2015-02-25 14:13:43

134

Views

A question regarding Silver's Theorem

Published on 25 Feb 2015 - 14:13

score 333 · Answer 15 · 2015-03-09 09:36:50

333

Views

An upper bound of a countable set of countable ordinals

Published on 09 Mar 2015 - 9:36

List Question

finite sequences,linear order, lexicographic order, well order, cardinal

Is $f: \mathcal{P}(\omega) \to \omega \cup \lbrace \omega \rbrace, \ x \mapsto \bigcup \lbrace n \in \omega: n \subset x \rbrace $ surjective?

Lexicographic order on $\alpha^\beta$ is well-ordered

How do we know that $\omega_1$ exists in ZF?

Does every countable sequence of ordinals converge?

A question about well-ordered subsets of partially ordered sets

Ordinals that are not cardinals

If $f\colon\kappa\rightarrow\kappa$, then the set of all $\alpha < \kappa$ such that $f(\xi) < \alpha$ for all $\xi < \alpha$ is closed and unbounded.

What is wrong with the following function $f:ON \rightarrow ON$?

Given stationary set $A$ of $k$, there exists an ordinals $\alpha$ such that $A$ contains all limit ordinals greater then $\alpha$

Do ordinal sets exist?

Theorem $($Transfinite Induction and Construction$)$ (James Dugundji - 5.1, Page - 40)

How to prove $cf(\aleph_{\omega_1})=\omega_1$?

A question regarding Silver's Theorem

An upper bound of a countable set of countable ordinals

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