Question

Do we need _strict_ monotonicity for the fixed point lemma for normal functions?

score 291 · Answer 1 · 2018-03-31 22:07:16

291

Views

Do we need _strict_ monotonicity for the fixed point lemma for normal functions?

Published on 31 Mar 2018 - 22:07

score 44 · Answer 2 · 2018-04-01 10:40:40

44

Views

2 different ordinals necessarily have the membership relation

Published on 01 Apr 2018 - 10:40

score 626 · Answer 3 · 2018-04-04 07:01:16

626

Views

(Intuition) how big is the church-kleene ordinal?

Published on 04 Apr 2018 - 7:01

score 454 · Answer 4 · 2026-03-22 22:54:08

454

Views

The Veblen Hierarchy named with uncountable ordinals vs ordinal collapsing functions

Published on 22 Mar 2026 - 22:54

score 82 · Answer 5 · 2018-04-16 00:27:29

82

Views

Proving any bounded family of ordinals has a supremum

Published on 16 Apr 2018 - 0:27

score 228 · Answer 6 · 2018-04-17 17:33:03

228

Views

Epsilon numbers: how to show $\varepsilon_{\omega_\alpha}=\omega_\alpha$ for $\alpha>0$?

Published on 17 Apr 2018 - 17:33

score 92 · Answer 7 · 2018-04-19 03:22:06

92

Views

Ordinal $\alpha$ is isomorphic to a proper initial segment of another ordinal $\beta \iff \alpha \in \beta$

Published on 19 Apr 2018 - 3:22

score 101 · Answer 8 · 2018-04-19 14:36:06

101

Views

Is the limit of a set of ordinals distinct from the ordinal of the union of sets up to the limit?

Published on 19 Apr 2018 - 14:36

score 810 · Answer 9 · 2026-03-22 12:34:52

810

Views

Show that ordinal addition is associative

Published on 22 Mar 2026 - 12:34

score 165 · Answer 10 · 2026-03-21 22:35:45

165

Views

How to order ordinal numbers

Published on 21 Mar 2026 - 22:35

score 385 · Answer 11 · 2018-04-23 07:01:40

385

Views

Show that any element of an ordinal is an initial segment of that ordinal

Published on 23 Apr 2018 - 7:01

score 253 · Answer 12 · 2018-04-23 19:33:51

253

Views

Prove $\alpha + \beta = \beta + \alpha \Rightarrow \alpha = \gamma n, \beta = \gamma m$ for some $m, n \in \mathbb{N}$.

Published on 23 Apr 2018 - 19:33

score 361 · Answer 13 · 2018-04-25 14:59:44

361

Views

Does $\alpha^{\omega}$ have a countable fixed point $\alpha>1$?

Published on 25 Apr 2018 - 14:59

score 390 · Answer 14 · 2018-04-25 19:18:00

390

Views

Is it possible to define a family of fundamental sequences for all countable (limit) ordinals? (Without AC)

Published on 25 Apr 2018 - 19:18

score 696 · Answer 15 · 2026-03-22 14:34:11

696

Views

Ordinal $\alpha$ such that $\alpha = \omega_{\alpha}$?

Published on 22 Mar 2026 - 14:34

List Question

Do we need _strict_ monotonicity for the fixed point lemma for normal functions?

2 different ordinals necessarily have the membership relation

(Intuition) how big is the church-kleene ordinal?

The Veblen Hierarchy named with uncountable ordinals vs ordinal collapsing functions

Proving any bounded family of ordinals has a supremum

Epsilon numbers: how to show $\varepsilon_{\omega_\alpha}=\omega_\alpha$ for $\alpha>0$?

Ordinal $\alpha$ is isomorphic to a proper initial segment of another ordinal $\beta \iff \alpha \in \beta$

Is the limit of a set of ordinals distinct from the ordinal of the union of sets up to the limit?

Show that ordinal addition is associative

How to order ordinal numbers

Show that any element of an ordinal is an initial segment of that ordinal

Prove $\alpha + \beta = \beta + \alpha \Rightarrow \alpha = \gamma n, \beta = \gamma m$ for some $m, n \in \mathbb{N}$.

Does $\alpha^{\omega}$ have a countable fixed point $\alpha>1$?

Is it possible to define a family of fundamental sequences for all countable (limit) ordinals? (Without AC)

Ordinal $\alpha$ such that $\alpha = \omega_{\alpha}$?

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