Question

Prove using transfinite induction that if ordinals $\alpha$ and $\beta$ are countable, then so is $\alpha + \beta$.

score 883 · Answer 1 · 2014-03-15 19:13:56

883

Views

Prove using transfinite induction that if ordinals $\alpha$ and $\beta$ are countable, then so is $\alpha + \beta$.

Published on 15 Mar 2014 - 19:13

score 230 · Answer 2 · 2014-03-16 10:53:06

230

Views

A canonical injection $f:\alpha\to[0,1]$ for an arbitrary countable ordinal $\alpha$

Published on 16 Mar 2014 - 10:53

score 596 · Answer 3 · 2014-03-16 17:14:52

596

Views

Why is it that $\omega + \omega_1 = \omega_1$?

Published on 16 Mar 2014 - 17:14

score 792 · Answer 4 · 2014-03-16 23:24:42

792

Views

Weak monotonicity of ordinal addition

Published on 16 Mar 2014 - 23:24

score 76 · Answer 5 · 2014-03-17 13:18:31

76

Views

Ordinal Arithmetic sufficient condition that a + c < b + c

Published on 17 Mar 2014 - 13:18

score 285 · Answer 6 · 2014-03-21 15:35:43

285

Views

Prove $\bigcup \omega_1 = \omega_1$

Published on 21 Mar 2014 - 15:35

score 80 · Answer 7 · 2014-03-23 15:35:48

80

Views

Existence of a function from ordinal to limit ordinal of the same cardinality

Published on 23 Mar 2014 - 15:35

score 717 · Answer 8 · 2026-03-25 03:04:06

717

Views

Definition of the function $f_{\epsilon_0}$ in the fast-growing hierachy

Published on 25 Mar 2026 - 3:04

score 66 · Answer 9 · 2014-04-10 21:23:11

66

Views

An alternative succinct proof needed for trivial cardinality fact

Published on 10 Apr 2014 - 21:23

score 185 · Answer 10 · 2014-04-16 13:48:59

185

Views

How many omegas are there in $\large f_{\varepsilon_0}$?

Published on 16 Apr 2014 - 13:48

score 473 · Answer 11 · 2026-03-25 03:06:58

473

Views

When does $f_{\omega+1}$ catch up the $G_n$-sequence?

Published on 25 Mar 2026 - 3:06

score 1k · Answer 12 · 2014-04-18 12:52:31

1k

Views

Ordinal addition is associative

Published on 18 Apr 2014 - 12:52

score 666 · Answer 13 · 2026-03-25 18:57:27

666

Views

Is there a subset of R such that its Cantor-Bendixson rank is the first limit ordinal?

Published on 25 Mar 2026 - 18:57

score 875 · Answer 14 · 2014-04-22 19:33:04

875

Views

Simplify this expression of ordinal numbers: $(ω+1) ω²$

Published on 22 Apr 2014 - 19:33

score 215 · Answer 15 · 2014-04-23 16:22:43

215

Views

Tarski's fixed point theorem

Published on 23 Apr 2014 - 16:22

List Question

Prove using transfinite induction that if ordinals $\alpha$ and $\beta$ are countable, then so is $\alpha + \beta$.

A canonical injection $f:\alpha\to[0,1]$ for an arbitrary countable ordinal $\alpha$

Why is it that $\omega + \omega_1 = \omega_1$?

Weak monotonicity of ordinal addition

Ordinal Arithmetic sufficient condition that a + c < b + c

Prove $\bigcup \omega_1 = \omega_1$

Existence of a function from ordinal to limit ordinal of the same cardinality

Definition of the function $f_{\epsilon_0}$ in the fast-growing hierachy

An alternative succinct proof needed for trivial cardinality fact

How many omegas are there in $\large f_{\varepsilon_0}$?

When does $f_{\omega+1}$ catch up the $G_n$-sequence?

Ordinal addition is associative

Is there a subset of R such that its Cantor-Bendixson rank is the first limit ordinal?

Simplify this expression of ordinal numbers: $(ω+1) ω²$

Tarski's fixed point theorem

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