Question

the Class of Ordinals is a set?

score 1.5k · Answer 1 · 2013-10-27 17:41:47

1.5k

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the Class of Ordinals is a set?

Published on 27 Oct 2013 - 17:41

score 150 · Answer 2 · 2013-10-27 17:54:25

150

Views

Can ordinals multiplication be defined by recursion?

Published on 27 Oct 2013 - 17:54

score 1.2k · Answer 3 · 2013-10-31 19:21:31

1.2k

Views

Showing ordinal addition and ordinal multiplication are defined

Published on 31 Oct 2013 - 19:21

score 346 · Answer 4 · 2013-11-01 08:39:35

346

Views

Ordinal inequalities

Published on 01 Nov 2013 - 8:39

score 146 · Answer 5 · 2013-11-05 01:30:33

146

Views

How to compute a Von Neumann Successor - ∪∪7?

Published on 05 Nov 2013 - 1:30

score 732 · Answer 6 · 2013-11-09 12:22:07

732

Views

Ordinals: if $\alpha < \omega^{\beta}$ then $\alpha + \omega^{\beta} = \omega^{\beta}$

Published on 09 Nov 2013 - 12:22

score 173 · Answer 7 · 2013-11-10 03:18:30

173

Views

$\alpha > \omega$ is an $\epsilon$-number iff $\beta^\gamma < \alpha, \forall \beta, \gamma < \alpha$

Published on 10 Nov 2013 - 3:18

score 634 · Answer 8 · 2013-11-11 08:43:34

634

Views

Proving, for every three ordinals $\alpha,\beta,$ and $\gamma$, that $\alpha^{\beta+\gamma}=\alpha^{\beta}\alpha^{\gamma}$

Published on 11 Nov 2013 - 8:43

score 144 · Answer 9 · 2013-11-12 14:15:13

144

Views

Functions from ordinals to ordinals

Published on 12 Nov 2013 - 14:15

score 45 · Answer 10 · 2013-11-14 08:02:44

45

Views

Existence of certain $\left\langle{\alpha_n | n \in \omega}\right\rangle$

Published on 14 Nov 2013 - 8:02

score 360 · Answer 11 · 2013-11-14 12:24:09

360

Views

Let $\gamma $ be an ordinal. Prove there is an ordering preserving $f:\gamma \to \mathbb{R}$ iff $\gamma < \omega_1.$

Published on 14 Nov 2013 - 12:24

score 81 · Answer 12 · 2013-11-15 07:52:07

81

Views

A representation of well-orderings?

Published on 15 Nov 2013 - 7:52

score 713 · Answer 13 · 2026-02-23 13:46:24

713

Views

Prove that if $\{K_n\}_{n\in\mathbb{N}}$ is a sequence of uncountable compact sets of $X$, then $\bigcap\limits_{n\in\mathbb{N}}K_n$ is uncountable

Published on 23 Feb 2026 - 13:46

score 69 · Answer 14 · 2013-11-24 22:23:37

69

Views

Prove that for any $m, n \in\omega$ that (i) $m + 0 = m$, (ii) $m + n^+ = (m + n)^+$

Published on 24 Nov 2013 - 22:23

score 85 · Answer 15 · 2013-11-25 21:20:37

85

Views

Reducing ordinals in the representation of a limit ordinal as $\bigcup_{\beta < \alpha} \beta$

Published on 25 Nov 2013 - 21:20

List Question

the Class of Ordinals is a set?

Can ordinals multiplication be defined by recursion?

Showing ordinal addition and ordinal multiplication are defined

Ordinal inequalities

How to compute a Von Neumann Successor - ∪∪7?

Ordinals: if $\alpha < \omega^{\beta}$ then $\alpha + \omega^{\beta} = \omega^{\beta}$

$\alpha > \omega$ is an $\epsilon$-number iff $\beta^\gamma < \alpha, \forall \beta, \gamma < \alpha$

Proving, for every three ordinals $\alpha,\beta,$ and $\gamma$, that $\alpha^{\beta+\gamma}=\alpha^{\beta}\alpha^{\gamma}$

Functions from ordinals to ordinals

Existence of certain $\left\langle{\alpha_n | n \in \omega}\right\rangle$

Let $\gamma $ be an ordinal. Prove there is an ordering preserving $f:\gamma \to \mathbb{R}$ iff $\gamma < \omega_1.$

A representation of well-orderings?

Prove that if $\{K_n\}_{n\in\mathbb{N}}$ is a sequence of uncountable compact sets of $X$, then $\bigcap\limits_{n\in\mathbb{N}}K_n$ is uncountable

Prove that for any $m, n \in\omega$ that (i) $m + 0 = m$, (ii) $m + n^+ = (m + n)^+$

Reducing ordinals in the representation of a limit ordinal as $\bigcup_{\beta < \alpha} \beta$

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