Question

If a linearly ordered set $L$ has the property that every order-preserving injection $L \rightarrow L$ is expansive, is $L$ necessarily well-ordered?

score 147 · Answer 1 · 2014-09-10 16:07:53

If a linearly ordered set $L$ has the property that every order-preserving injection $L \rightarrow L$ is expansive, is $L$ necessarily well-ordered?

score 715 · Answer 2 · 2014-09-16 09:27:22

A limit ordinal $\gamma$ is indecomposable if and only if $\alpha + \gamma = \gamma$ if and only if $\gamma = \omega^{\alpha}$ for some $\alpha$.

score 240 · Answer 3 · 2014-09-16 15:35:35

240

Views

For every ordinal $\alpha$, there is a cardinal number greater then $\alpha$.

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score 66 · Answer 5 · 2026-03-25 04:40:19

66

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'Popular mathematics' resource about infinite ordinals

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score 809 · Answer 6 · 2014-09-23 08:04:04

809

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show that ordinal multiplication is associative

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score 790 · Answer 7 · 2014-09-26 07:00:06

790

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Definition of continuity of ordinal function

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score 73 · Answer 8 · 2014-09-28 22:43:15

73

Views

Ordinal arithmetic and functions

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score 96 · Answer 9 · 2014-09-29 05:58:40

96

Views

In what sense $\alpha \times \alpha$ is the initial segment generated by $(0,\alpha)$ in $Ord \times Ord$?

Published on 29 Sep 2014 - 5:58

score 2.1k · Answer 10 · 2014-09-29 13:07:33

2.1k

Views

Prove that ordinal multiplication is left distributive

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score 53 · Answer 11 · 2014-09-30 15:14:57

53

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Cardinality: is it true that $|X^\mathcal{inj}| \leq 2^{|X|}$?

Published on 30 Sep 2014 - 15:14

score 2.7k · Answer 12 · 2014-10-03 11:36:09

2.7k

Views

An easy to understand definition of $\omega_1$?

Published on 03 Oct 2014 - 11:36

score 161 · Answer 13 · 2014-10-08 09:32:57

161

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What is the smallest infinite ordinal that is not order isomorphic to a reordering of the natural numbers?

Published on 08 Oct 2014 - 9:32

score 280 · Answer 14 · 2014-10-10 13:05:46

280

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A few questions on $\omega_1$

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score 186 · Answer 15 · 2014-10-13 19:12:12

186

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Comprehending ordinals: from $\omega^\omega$ through $\omega^{\omega^2}$ to $\varepsilon_0$

Published on 13 Oct 2014 - 19:12

List Question

If a linearly ordered set $L$ has the property that every order-preserving injection $L \rightarrow L$ is expansive, is $L$ necessarily well-ordered?

A limit ordinal $\gamma$ is indecomposable if and only if $\alpha + \gamma = \gamma$ if and only if $\gamma = \omega^{\alpha}$ for some $\alpha$.

For every ordinal $\alpha$, there is a cardinal number greater then $\alpha$.

There is a well ordering of the class of all finite sequences of ordinals

'Popular mathematics' resource about infinite ordinals

show that ordinal multiplication is associative

Definition of continuity of ordinal function

Ordinal arithmetic and functions

In what sense $\alpha \times \alpha$ is the initial segment generated by $(0,\alpha)$ in $Ord \times Ord$?

Prove that ordinal multiplication is left distributive

Cardinality: is it true that $|X^\mathcal{inj}| \leq 2^{|X|}$?

An easy to understand definition of $\omega_1$?

What is the smallest infinite ordinal that is not order isomorphic to a reordering of the natural numbers?

A few questions on $\omega_1$

Comprehending ordinals: from $\omega^\omega$ through $\omega^{\omega^2}$ to $\varepsilon_0$

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