Question

If $\gamma$ is an uncountable ordinal, then $\gamma$ contains uncountably many successor ordinals.

score 91 · Answer 1 · 2013-06-19 18:35:36

91

Views

If $\gamma$ is an uncountable ordinal, then $\gamma$ contains uncountably many successor ordinals.

Published on 19 Jun 2013 - 18:35

score 565 · Answer 2 · 2013-06-19 19:28:22

565

Views

Is $\alpha + \omega$ limit ordinal

Published on 19 Jun 2013 - 19:28

score 90 · Answer 3 · 2013-06-20 01:36:41

90

Views

Let $\alpha$ be an ordinal then $\alpha=\cup\alpha$ or $\alpha=s(\cup\alpha)$.

Published on 20 Jun 2013 - 1:36

score 283 · Answer 4 · 2013-06-20 12:51:39

283

Views

This set of ordinals is $\in$-transitive?

Published on 20 Jun 2013 - 12:51

score 204 · Answer 5 · 2013-06-21 20:13:31

204

Views

The concept of ordinals

Published on 21 Jun 2013 - 20:13

score 2.3k · Answer 6 · 2013-06-24 14:47:40

2.3k

Views

show that every continuous real-valued function defined on $S_{\mathbb{\Omega}}$ is eventually constant

Published on 24 Jun 2013 - 14:47

score 187 · Answer 7 · 2013-06-26 12:49:14

187

Views

Why are the ordinal operations defined that way?

Published on 26 Jun 2013 - 12:49

score 479 · Answer 8 · 2013-06-26 19:47:06

479

Views

Set $A$ has the cardinality of $\aleph_0$. Prove some properties of partial order $ \langle \mathcal P (A), \subseteq \rangle$.

Published on 26 Jun 2013 - 19:47

score 236 · Answer 9 · 2013-07-01 11:13:01

236

Views

Cardinal numbers

Published on 01 Jul 2013 - 11:13

score 142 · Answer 10 · 2013-07-01 14:10:35

142

Views

Are the closed ordinals (apart from $0$ and $1$) precisely the regular cardinals?

Published on 01 Jul 2013 - 14:10

score 104 · Answer 11 · 2013-07-01 20:59:47

104

Views

Why is $n+\omega=\omega$ for finite $n$?

Published on 01 Jul 2013 - 20:59

score 131 · Answer 12 · 2013-07-02 09:14:32

131

Views

Statements regarding ordinal numbers

Published on 02 Jul 2013 - 9:14

score 763 · Answer 13 · 2013-07-03 01:28:47

763

Views

The limit elements of well-ordered proper classes

Published on 03 Jul 2013 - 1:28

score 209 · Answer 14 · 2013-07-07 11:30:30

209

Views

Does every countable subset of the set of all countable limit ordinals have the least upper bound in it?

Published on 07 Jul 2013 - 11:30

score 438 · Answer 15 · 2013-07-07 14:32:51

438

Views

Is there a nice characterization of posets induced by trees?

Published on 07 Jul 2013 - 14:32

List Question

If $\gamma$ is an uncountable ordinal, then $\gamma$ contains uncountably many successor ordinals.

Is $\alpha + \omega$ limit ordinal

Let $\alpha$ be an ordinal then $\alpha=\cup\alpha$ or $\alpha=s(\cup\alpha)$.

This set of ordinals is $\in$-transitive?

The concept of ordinals

show that every continuous real-valued function defined on $S_{\mathbb{\Omega}}$ is eventually constant

Why are the ordinal operations defined that way?

Set $A$ has the cardinality of $\aleph_0$. Prove some properties of partial order $ \langle \mathcal P (A), \subseteq \rangle$.

Cardinal numbers

Are the closed ordinals (apart from $0$ and $1$) precisely the regular cardinals?

Why is $n+\omega=\omega$ for finite $n$?

Statements regarding ordinal numbers

The limit elements of well-ordered proper classes

Does every countable subset of the set of all countable limit ordinals have the least upper bound in it?

Is there a nice characterization of posets induced by trees?

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