Question

How does the supremum of the cardinalities of a set of ordinals relate to the supremum of the ordinals?

score 1k · Answer 1 · 2012-08-21 06:47:32

1k

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How does the supremum of the cardinalities of a set of ordinals relate to the supremum of the ordinals?

Published on 21 Aug 2012 - 6:47

score 1.1k · Answer 2 · 2012-08-21 17:41:09

1.1k

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Which algebraic structure captures the ordinal arithmetic?

Published on 21 Aug 2012 - 17:41

score 824 · Answer 3 · 2012-08-24 07:44:30

824

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Does there exist a prime number decomposition for ordinal numbers?

Published on 24 Aug 2012 - 7:44

score 616 · Answer 4 · 2012-08-24 11:42:24

616

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If $\kappa$ is a cardinal, $\aleph$ is any $\aleph$-number, and if $\kappa\leq\aleph$ then $\kappa$ can be well ordered as well.

Published on 24 Aug 2012 - 11:42

score 305 · Answer 5 · 2012-08-26 14:10:27

305

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What is the name of $V_\alpha$?

Published on 26 Aug 2012 - 14:10

score 1.4k · Answer 6 · 2012-08-26 14:33:16

1.4k

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How do I show there isn't an order isomorphism b/w the two sets $\{1, 2, 3,...\}$ and $\{1, 2, 3, ..., \omega \}$

Published on 26 Aug 2012 - 14:33

score 1.2k · Answer 7 · 2012-09-02 14:36:49

1.2k

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Discussion: Differing definitions for the rank of a set

Published on 02 Sep 2012 - 14:36

score 3.6k · Answer 8 · 2012-09-04 12:27:41

3.6k

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How to prove that the set of all countable ordinals, $\omega_1$, is uncountable / has the cardinality $\aleph_1$?

Published on 04 Sep 2012 - 12:27

score 436 · Answer 9 · 2012-09-07 14:40:37

436

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Question on a proof from Jech's Set Theory of: If $X$ is a set of cardinals, then $\sup X$ is a cardinal.

Published on 07 Sep 2012 - 14:40

score 228 · Answer 10 · 2012-09-10 19:20:44

228

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Limit ordinals vs. Points at infinity

Published on 10 Sep 2012 - 19:20

score 2.8k · Answer 11 · 2026-03-26 02:51:28

2.8k

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What does $\upharpoonright$ in $G(F\upharpoonright\alpha)$ mean?

Published on 26 Mar 2026 - 2:51

score 637 · Answer 12 · 2012-09-16 11:27:33

637

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Why would the axiom of choice be needed if ordinals are well-ordered without AC?

Published on 16 Sep 2012 - 11:27

score 370 · Answer 13 · 2012-09-16 16:13:25

370

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Generalization of ordinals to well-founded sets?

Published on 16 Sep 2012 - 16:13

score 3.3k · Answer 14 · 2012-09-17 04:05:20

3.3k

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How to define countability of $\omega^{\omega}$ and $\omega_1$? in set theory?

Published on 17 Sep 2012 - 4:05

score 744 · Answer 15 · 2012-09-17 04:21:15

744

Views

How to prove that $\epsilon_0$ exists?

Published on 17 Sep 2012 - 4:21

List Question

How does the supremum of the cardinalities of a set of ordinals relate to the supremum of the ordinals?

Which algebraic structure captures the ordinal arithmetic?

Does there exist a prime number decomposition for ordinal numbers?

If $\kappa$ is a cardinal, $\aleph$ is any $\aleph$-number, and if $\kappa\leq\aleph$ then $\kappa$ can be well ordered as well.

What is the name of $V_\alpha$?

How do I show there isn't an order isomorphism b/w the two sets $\{1, 2, 3,...\}$ and $\{1, 2, 3, ..., \omega \}$

Discussion: Differing definitions for the rank of a set

How to prove that the set of all countable ordinals, $\omega_1$, is uncountable / has the cardinality $\aleph_1$?

Question on a proof from Jech's Set Theory of: If $X$ is a set of cardinals, then $\sup X$ is a cardinal.

Limit ordinals vs. Points at infinity

What does $\upharpoonright$ in $G(F\upharpoonright\alpha)$ mean?

Why would the axiom of choice be needed if ordinals are well-ordered without AC?

Generalization of ordinals to well-founded sets?

How to define countability of $\omega^{\omega}$ and $\omega_1$? in set theory?

How to prove that $\epsilon_0$ exists?

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