Question

A subspace of $\omega_1$ is metrizable iff it is nonstationary

score 314 · Answer 1 · 2017-04-12 21:05:44

314

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A subspace of $\omega_1$ is metrizable iff it is nonstationary

Published on 12 Apr 2017 - 21:05

score 65 · Answer 2 · 2017-04-18 03:08:18

65

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General formula involving ordinals

Published on 18 Apr 2017 - 3:08

score 133 · Answer 3 · 2017-04-20 18:06:25

133

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Prove that if $S$ be a subset of $Ord$. Show that $Ord\setminus S$ is order-isomorphic to $Ord$

Published on 20 Apr 2017 - 18:06

score 125 · Answer 4 · 2017-04-20 18:33:00

125

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Prove $ α + β = β$ if and only if $αω ≤ β$

Published on 20 Apr 2017 - 18:33

score 223 · Answer 5 · 2017-04-21 00:14:54

223

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Ordinal arithmetic help

Published on 21 Apr 2017 - 0:14

score 392 · Answer 6 · 2017-04-21 12:36:00

392

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Proving that for any ordinal $\alpha$, ordinal exponentiation satisfies $\alpha \cdot \alpha^\omega =\alpha^\omega$

Published on 21 Apr 2017 - 12:36

score 54 · Answer 7 · 2026-03-25 13:57:02

54

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How to use induction to prove that if $α+β=β$, then for every $n<ω,α⋅n\le β$ and hence $\alpha\omega\le \beta$?

Published on 25 Mar 2026 - 13:57

score 58 · Answer 8 · 2017-04-22 18:01:46

58

Views

Prove there cannot be an injection $f:Ord$ \ $T \to U$ for any set $U$.

Published on 22 Apr 2017 - 18:01

score 150 · Answer 9 · 2017-04-22 18:40:13

150

Views

Prove that if $\alpha+\beta=\beta$, then $\alpha\le \beta$

Published on 22 Apr 2017 - 18:40

score 803 · Answer 10 · 2017-04-22 19:22:41

803

Views

Long line with large uncountable ordinals

Published on 22 Apr 2017 - 19:22

score 59 · Answer 11 · 2017-04-23 03:32:24

59

Views

Proof verification: For any ordinals $\gamma,\beta$, $\gamma\le \gamma+\beta$.

Published on 23 Apr 2017 - 3:32

score 41 · Answer 12 · 2017-04-23 04:08:07

41

Views

Prove that for any ordinals $\gamma,\beta$, $\gamma\le \gamma+\beta$.

Published on 23 Apr 2017 - 4:08

score 384 · Answer 13 · 2026-04-01 14:20:17

384

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Transfinite Guessing Game

Published on 01 Apr 2026 - 14:20

score 197 · Answer 14 · 2017-04-25 03:19:08

197

Views

Prove any proper initial segment of $Ord\setminus S$ is a set.

Published on 25 Apr 2017 - 3:19

score 176 · Answer 15 · 2017-04-29 19:45:45

176

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Trees and ordinals

Published on 29 Apr 2017 - 19:45

List Question

A subspace of $\omega_1$ is metrizable iff it is nonstationary

General formula involving ordinals

Prove that if $S$ be a subset of $Ord$. Show that $Ord\setminus S$ is order-isomorphic to $Ord$

Prove $ α + β = β$ if and only if $αω ≤ β$

Ordinal arithmetic help

Proving that for any ordinal $\alpha$, ordinal exponentiation satisfies $\alpha \cdot \alpha^\omega =\alpha^\omega$

How to use induction to prove that if $α+β=β$, then for every $n<ω,α⋅n\le β$ and hence $\alpha\omega\le \beta$?

Prove there cannot be an injection $f:Ord$ \ $T \to U$ for any set $U$.

Prove that if $\alpha+\beta=\beta$, then $\alpha\le \beta$

Long line with large uncountable ordinals

Proof verification: For any ordinals $\gamma,\beta$, $\gamma\le \gamma+\beta$.

Prove that for any ordinals $\gamma,\beta$, $\gamma\le \gamma+\beta$.

Transfinite Guessing Game

Prove any proper initial segment of $Ord\setminus S$ is a set.

Trees and ordinals

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