Question

How to prove the Milner-Rado Paradox?

score 1k · Answer 1 · 2013-07-10 04:57:53

1k

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How to prove the Milner-Rado Paradox?

Published on 10 Jul 2013 - 4:57

score 835 · Answer 2 · 2013-07-14 11:28:50

835

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Why $\omega$ can't be bijectively mapped to $\omega +1$

Published on 14 Jul 2013 - 11:28

score 764 · Answer 3 · 2013-07-14 15:10:37

764

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If $\alpha$ is an ordinal, proving that $\alpha\cup\{\alpha\}$ is an ordinal.

Published on 14 Jul 2013 - 15:10

score 461 · Answer 4 · 2013-07-16 10:49:31

461

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Is there any countable ordinal number which has a member undefinable?

Published on 16 Jul 2013 - 10:49

score 168 · Answer 5 · 2013-07-17 02:56:55

168

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Prove that if $x,y\in\alpha$, then $x<y,x>y$ or $x=y$.

Published on 17 Jul 2013 - 2:56

score 968 · Answer 6 · 2026-03-27 02:36:10

968

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If $(W,<)$ is a well-ordered set and $f : W \rightarrow W$ is an increasing function, then $f(x) ≥ x$ for each $x \in W$

Published on 27 Mar 2026 - 2:36

score 157 · Answer 7 · 2026-03-30 06:50:00

157

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Definition of ordinals in Grothendieck toposes

Published on 30 Mar 2026 - 6:50

score 289 · Answer 8 · 2013-07-21 06:20:54

289

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How can we describe different sorts of limits using ordinals, and what kind of "work" can they do in transfinite induction?

Published on 21 Jul 2013 - 6:20

score 488 · Answer 9 · 2013-07-21 11:33:48

488

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I read that ordinal numbers relate to length, while cardinal numbers relate to size. How do 'length' and 'size' differ?

Published on 21 Jul 2013 - 11:33

score 941 · Answer 10 · 2013-07-26 11:52:10

941

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Ordinal arithmetic exercise in Kunen

Published on 26 Jul 2013 - 11:52

score 233 · Answer 11 · 2013-07-29 18:07:24

233

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AC iff $P(\delta)$ can be well-ordered for all $\delta\in{\bf On}$

Published on 29 Jul 2013 - 18:07

score 219 · Answer 12 · 2013-07-30 17:36:00

219

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$X = [ 0,\omega_1 )$ is maximal countably compact

Published on 30 Jul 2013 - 17:36

score 572 · Answer 13 · 2013-08-04 04:22:07

572

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The preorder of countable order types

Published on 04 Aug 2013 - 4:22

score 4k · Answer 14 · 2013-08-06 21:58:22

4k

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Cardinal Arithmetic versus Ordinal Arithmetic

Published on 06 Aug 2013 - 21:58

score 2.7k · Answer 15 · 2013-08-08 18:27:41

2.7k

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The order type of the rationals.

Published on 08 Aug 2013 - 18:27

List Question

How to prove the Milner-Rado Paradox?

Why $\omega$ can't be bijectively mapped to $\omega +1$

If $\alpha$ is an ordinal, proving that $\alpha\cup\{\alpha\}$ is an ordinal.

Is there any countable ordinal number which has a member undefinable?

Prove that if $x,y\in\alpha$, then $x<y,x>y$ or $x=y$.

If $(W,<)$ is a well-ordered set and $f : W \rightarrow W$ is an increasing function, then $f(x) ≥ x$ for each $x \in W$

Definition of ordinals in Grothendieck toposes

How can we describe different sorts of limits using ordinals, and what kind of "work" can they do in transfinite induction?

I read that ordinal numbers relate to length, while cardinal numbers relate to size. How do 'length' and 'size' differ?

Ordinal arithmetic exercise in Kunen

AC iff $P(\delta)$ can be well-ordered for all $\delta\in{\bf On}$

$X = [ 0,\omega_1 )$ is maximal countably compact

The preorder of countable order types

Cardinal Arithmetic versus Ordinal Arithmetic

The order type of the rationals.

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