Question

What are possible ways to refer to a particular (unique) real number that encodes a copy of a chosen large countable ordinal?

score 118 · Answer 1 · 2026-04-14 05:32:17

What are possible ways to refer to a particular (unique) real number that encodes a copy of a chosen large countable ordinal?

score 288 · Answer 2 · 2026-04-12 17:52:54

288

Views

What are the order types of all the total orders on $\mathbb{N}$?

Published on 12 Apr 2026 - 17:52

score 392 · Answer 3 · 2026-04-14 20:22:35

392

Views

Is there a standard notation for an ordinal number with cardinality of the continuum?

Published on 14 Apr 2026 - 20:22

score 991 · Answer 4 · 2026-04-13 00:53:35

991

Views

Why does $1+\omega=\omega$ with ordinal addition

Published on 13 Apr 2026 - 0:53

score 123 · Answer 5 · 2026-04-08 20:12:38

123

Views

Given an ordinal $(\alpha,\in)$, how do I find a subset of rationals which is isomorphic to it?

Published on 08 Apr 2026 - 20:12

score 580 · Answer 6 · 2026-04-14 07:04:16

580

Views

Show that $\omega + \omega$ is countable.

Published on 14 Apr 2026 - 7:04

score 248 · Answer 7 · 2026-04-13 12:57:34

248

Views

The intersection of a class of ordinals belongs to that class

Published on 13 Apr 2026 - 12:57

score 52 · Answer 8 · 2026-04-30 14:29:18

52

Views

Linearity of ordinals

Published on 30 Apr 2026 - 14:29

score 583 · Answer 9 · 2026-05-10 16:01:09

583

Views

Sequential compactness of $S_\Omega$ and unbounded sequences.

Published on 10 May 2026 - 16:01

score 231 · Answer 10 · 2026-05-10 14:57:02

231

Views

Is there a standard ordering of non-ordinal order types?

Published on 10 May 2026 - 14:57

score 287 · Answer 11 · 2026-04-12 23:52:58

287

Views

What is the cardinality of the set of equivalence classes of countable order types under bi-embeddability?

Published on 12 Apr 2026 - 23:52

score 202 · Answer 12 · 2026-04-12 08:42:57

202

Views

Are ordinals greater than $\varepsilon_0$ used outside Ordinal Analysis?

Published on 12 Apr 2026 - 8:42

score 31 · Answer 13 · 2026-04-16 19:31:41

31

Views

If $\alpha$ and $\beta$ are ordinals. Then $\gamma=\alpha\cap\beta$ is an ordinal

Published on 16 Apr 2026 - 19:31

score 793 · Answer 14 · 2026-04-11 11:57:13

793

Views

Every set of ordinals is well-ordered with respect to $\in$

Published on 11 Apr 2026 - 11:57

score 40 · Answer 15 · 2026-04-15 23:20:18

40

Views

Suppose that $X$ is a set of ordinals. Then $\bigcup X$ is transitive

Published on 15 Apr 2026 - 23:20

List Question

What are possible ways to refer to a particular (unique) real number that encodes a copy of a chosen large countable ordinal?

What are the order types of all the total orders on $\mathbb{N}$?

Is there a standard notation for an ordinal number with cardinality of the continuum?

Why does $1+\omega=\omega$ with ordinal addition

Given an ordinal $(\alpha,\in)$, how do I find a subset of rationals which is isomorphic to it?

Show that $\omega + \omega$ is countable.

The intersection of a class of ordinals belongs to that class

Linearity of ordinals

Sequential compactness of $S_\Omega$ and unbounded sequences.

Is there a standard ordering of non-ordinal order types?

What is the cardinality of the set of equivalence classes of countable order types under bi-embeddability?

Are ordinals greater than $\varepsilon_0$ used outside Ordinal Analysis?

If $\alpha$ and $\beta$ are ordinals. Then $\gamma=\alpha\cap\beta$ is an ordinal

Every set of ordinals is well-ordered with respect to $\in$

Suppose that $X$ is a set of ordinals. Then $\bigcup X$ is transitive

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