Question

There are arbitrary large singular cardinals $\aleph_\alpha$ such that $\aleph_\alpha=\alpha$

score 553 · Answer 1 · 2018-12-08 14:52:41

553

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There are arbitrary large singular cardinals $\aleph_\alpha$ such that $\aleph_\alpha=\alpha$

Published on 08 Dec 2018 - 14:52

score 65 · Answer 2 · 2018-12-09 01:24:30

65

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If $\aleph_\alpha=\alpha$, then $\alpha$ is a limit ordinal

Published on 09 Dec 2018 - 1:24

score 95 · Answer 3 · 2018-12-11 05:36:16

95

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Proving $\alpha+\beta=\sup\{\alpha+\beta_{\delta}:\delta<\gamma\}$

Published on 11 Dec 2018 - 5:36

score 615 · Answer 4 · 2018-12-13 08:37:54

615

Views

How do you define ordinal exponentiation without induction?

Published on 13 Dec 2018 - 8:37

score 141 · Answer 5 · 2026-03-25 06:24:28

141

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Difference between Kleene's O and the system $S_1$

Published on 25 Mar 2026 - 6:24

score 82 · Answer 6 · 2018-12-15 14:13:34

82

Views

Beginning a Veblen heirarchy with $1 + x$?

Published on 15 Dec 2018 - 14:13

score 57 · Answer 7 · 2026-03-25 14:19:23

57

Views

$\leq_{\frak K_\lambda}$-increasing continuous

Published on 25 Mar 2026 - 14:19

score 972 · Answer 8 · 2026-03-25 06:21:38

972

Views

Pardon my ignorance, but isn't TREE(3) a finite number?

Published on 25 Mar 2026 - 6:21

score 130 · Answer 9 · 2026-03-25 22:04:59

130

Views

What is a simple method of combining an infinite (or finite) set of well-orders into one well-order?

Published on 25 Mar 2026 - 22:04

score 106 · Answer 10 · 2018-12-20 04:23:26

What is the name of a theorem which says that if $\alpha$ and $\beta$ are ordinals, then $\alpha\in\beta$, or $\beta\in\alpha$, or $\alpha=\beta$?

score 66 · Answer 11 · 2018-12-21 19:34:19

66

Views

Boolean algebras/Unknown notation

Published on 21 Dec 2018 - 19:34

score 55 · Answer 12 · 2018-12-21 22:45:41

55

Views

Let $B,C$ be sets, $B\subseteq C$ such that $\forall c∈C,\exists b\in B: c\le b$ then $\sup B=\sup C$.

Published on 21 Dec 2018 - 22:45

score 1k · Answer 13 · 2026-03-25 15:42:24

1k

Views

What exactly does it mean for an Infinite Time Turing Machine to reach stage $\omega$ (and limit ordinal stage)?

Published on 25 Mar 2026 - 15:42

score 110 · Answer 14 · 2018-12-25 11:54:39

110

Views

Is this an equivalent definition of singular cardinal?

Published on 25 Dec 2018 - 11:54

score 345 · Answer 15 · 2018-12-26 15:44:51

345

Views

If $\alpha$ is a limit ordinal, then $\operatorname{cf}(\alpha)$ is a limit ordinal

Published on 26 Dec 2018 - 15:44

List Question

There are arbitrary large singular cardinals $\aleph_\alpha$ such that $\aleph_\alpha=\alpha$

If $\aleph_\alpha=\alpha$, then $\alpha$ is a limit ordinal

Proving $\alpha+\beta=\sup\{\alpha+\beta_{\delta}:\delta<\gamma\}$

How do you define ordinal exponentiation without induction?

Difference between Kleene's O and the system $S_1$

Beginning a Veblen heirarchy with $1 + x$?

$\leq_{\frak K_\lambda}$-increasing continuous

Pardon my ignorance, but isn't TREE(3) a finite number?

What is a simple method of combining an infinite (or finite) set of well-orders into one well-order?

What is the name of a theorem which says that if $\alpha$ and $\beta$ are ordinals, then $\alpha\in\beta$, or $\beta\in\alpha$, or $\alpha=\beta$?

Boolean algebras/Unknown notation

Let $B,C$ be sets, $B\subseteq C$ such that $\forall c∈C,\exists b\in B: c\le b$ then $\sup B=\sup C$.

What exactly does it mean for an Infinite Time Turing Machine to reach stage $\omega$ (and limit ordinal stage)?

Is this an equivalent definition of singular cardinal?

If $\alpha$ is a limit ordinal, then $\operatorname{cf}(\alpha)$ is a limit ordinal

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