Question

What is the rank of the set of functions from $\omega$ to $\omega$?

score 175 · Answer 1 · 2020-11-21 20:09:51

175

Views

What is the rank of the set of functions from $\omega$ to $\omega$?

Published on 21 Nov 2020 - 20:09

score 117 · Answer 2 · 2020-11-26 17:02:52

117

Views

Ordinal numbers arithmetic $((1 + \omega) + \omega) \cdot \omega$ Cantor Normal Form

Published on 26 Nov 2020 - 17:02

score 96 · Answer 3 · 2020-11-26 18:14:00

96

Views

Ordinal numbers arithmetic $((\omega + 1) + (\omega + 1))^\omega$ Cantor Normalform

Published on 26 Nov 2020 - 18:14

score 122 · Answer 4 · 2020-11-29 17:59:38

Ordinal arithmetic $(2\cdot (\omega+1))\cdot \omega$ and $\gamma = \bigcup \{\omega, \omega^\omega, \omega^{\omega^\omega}\}$ Cantor Normalform

score 57 · Answer 5 · 2026-03-27 22:03:25

57

Views

Confusion Regarding Notation in a Proof about two Well-Ordered Sets

Published on 27 Mar 2026 - 22:03

score 69 · Answer 6 · 2026-03-31 21:01:42

69

Views

Equational theory of $\varepsilon_0$ under the signature $(+,*,exp,0,1)$

Published on 31 Mar 2026 - 21:01

score 142 · Answer 7 · 2020-12-04 18:11:03

142

Views

$[0,\omega_1]$ is not first countable.

Published on 04 Dec 2020 - 18:11

score 120 · Answer 8 · 2020-12-07 08:42:55

120

Views

How to construct an increasing sequence in an ordinal $\alpha$ from a bijection $f: |\alpha| \rightarrow \alpha$

Published on 07 Dec 2020 - 8:42

score 173 · Answer 9 · 2020-12-08 04:07:33

173

Views

Every countable ordinal is isomorphic to a set of rationals

Published on 08 Dec 2020 - 4:07

score 151 · Answer 10 · 2020-12-15 12:06:54

151

Views

Understanding the differences between $\omega + 1$ and $1 + \omega$ using Kenneth Kunen's definition of Ordinal Addition

Published on 15 Dec 2020 - 12:06

score 154 · Answer 11 · 2020-12-18 13:51:41

154

Views

How do I create the set necessary to prove the following statement: If $X$ is a non-empty set of ordinals, then $\bigcup X = \text{sup}(X)$

Published on 18 Dec 2020 - 13:51

score 96 · Answer 12 · 2026-03-30 23:10:02

96

Views

Proving that $\mathbb{N}$ is well-ordered without appealing to induction.

Published on 30 Mar 2026 - 23:10

score 28 · Answer 13 · 2020-12-24 19:07:01

28

Views

Is this proposition regarding equipotence true, without the needing axiom of choice?

Published on 24 Dec 2020 - 19:07

score 209 · Answer 14 · 2020-12-27 20:16:41

209

Views

Verify proof that limit ordinal iff $\alpha = \cup_{\beta<\alpha} \beta$.

Published on 27 Dec 2020 - 20:16

score 105 · Answer 15 · 2026-03-26 22:15:10

105

Views

What is the intuitive reason why there is no recursively related notation-system which gives a name to every constructive ordinal?

Published on 26 Mar 2026 - 22:15

List Question

What is the rank of the set of functions from $\omega$ to $\omega$?

Ordinal numbers arithmetic $((1 + \omega) + \omega) \cdot \omega$ Cantor Normal Form

Ordinal numbers arithmetic $((\omega + 1) + (\omega + 1))^\omega$ Cantor Normalform

Ordinal arithmetic $(2\cdot (\omega+1))\cdot \omega$ and $\gamma = \bigcup \{\omega, \omega^\omega, \omega^{\omega^\omega}\}$ Cantor Normalform

Confusion Regarding Notation in a Proof about two Well-Ordered Sets

Equational theory of $\varepsilon_0$ under the signature $(+,*,exp,0,1)$

$[0,\omega_1]$ is not first countable.

How to construct an increasing sequence in an ordinal $\alpha$ from a bijection $f: |\alpha| \rightarrow \alpha$

Every countable ordinal is isomorphic to a set of rationals

Understanding the differences between $\omega + 1$ and $1 + \omega$ using Kenneth Kunen's definition of Ordinal Addition

How do I create the set necessary to prove the following statement: If $X$ is a non-empty set of ordinals, then $\bigcup X = \text{sup}(X)$

Proving that $\mathbb{N}$ is well-ordered without appealing to induction.

Is this proposition regarding equipotence true, without the needing axiom of choice?

Verify proof that limit ordinal iff $\alpha = \cup_{\beta<\alpha} \beta$.

What is the intuitive reason why there is no recursively related notation-system which gives a name to every constructive ordinal?

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