Question

Proving that $\omega_1$ is a limit ordinal

score 399 · Answer 1 · 2026-04-10 03:43:30

399

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Proving that $\omega_1$ is a limit ordinal

Published on 10 Apr 2026 - 3:43

score 404 · Answer 2 · 2026-04-17 02:17:43

404

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If $\alpha$ is an ordinal set and $\beta\in\alpha$ then $\beta$ is an ordinal set also

Published on 17 Apr 2026 - 2:17

score 254 · Answer 3 · 2026-04-13 16:29:57

254

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How symmetric is the hierarchy of indecomposable ordinals?

Published on 13 Apr 2026 - 16:29

score 165 · Answer 4 · 2026-04-14 09:12:48

165

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If $A$ is a set of ordinals then $\bigcup A=\sup A$

Published on 14 Apr 2026 - 9:12

score 768 · Answer 5 · 2026-05-05 16:33:55

768

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About the proof that an infinite ordinal has the same cardinality as its successor

Published on 05 May 2026 - 16:33

score 666 · Answer 6 · 2026-04-13 13:42:19

666

Views

Why do we define ordinals the way we do?

Published on 13 Apr 2026 - 13:42

score 233 · Answer 7 · 2026-04-16 23:30:48

233

Views

Find ordinal numbers $a$, $b$ and $c$ so that $(a\cdot b)^c$ is not equal to $a^c \cdot b^c$

Published on 16 Apr 2026 - 23:30

score 752 · Answer 8 · 2026-04-15 20:46:30

752

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Set theory ordinals problem Prove that if $b$ is a limit ordinal and $a<b$ then $a+b=b$ (a is any ordinal number)

Published on 15 Apr 2026 - 20:46

score 213 · Answer 9 · 2026-04-09 11:01:13

213

Views

Suggestion for a textbook including Von Neumann definition of ordinal numbers

Published on 09 Apr 2026 - 11:01

score 80 · Answer 10 · 2026-04-15 20:51:42

80

Views

Do we need Axiom of Regularity to prove that $a=\{x,\{x\}\}\text{ is an ordinal }\implies x=\emptyset$?

Published on 15 Apr 2026 - 20:51

score 153 · Answer 11 · 2026-04-13 16:14:15

153

Views

Let $X$ be a non-empty set of ordinals. What are the necessary and sufficient conditions for $X$ to be an ordinal?

Published on 13 Apr 2026 - 16:14

score 274 · Answer 12 · 2026-04-16 20:05:46

274

Views

For any two ordinals $x$ and $y$, either $x\in y$, or $x=y$, or $y\in x$

Published on 16 Apr 2026 - 20:05

score 96 · Answer 13 · 2026-04-15 02:00:54

96

Views

Double induction on ordinals (If $\ \alpha+1=\beta+1$ then $\alpha=\beta$)

Published on 15 Apr 2026 - 2:00

score 665 · Answer 14 · 2026-05-10 14:51:52

665

Views

isomorphism from well ordered set to ordinal

Published on 10 May 2026 - 14:51

score 330 · Answer 15 · 2026-04-16 14:37:02

330

Views

Union of a set of ordinals

Published on 16 Apr 2026 - 14:37

List Question

Proving that $\omega_1$ is a limit ordinal

If $\alpha$ is an ordinal set and $\beta\in\alpha$ then $\beta$ is an ordinal set also

How symmetric is the hierarchy of indecomposable ordinals?

If $A$ is a set of ordinals then $\bigcup A=\sup A$

About the proof that an infinite ordinal has the same cardinality as its successor

Why do we define ordinals the way we do?

Find ordinal numbers $a$, $b$ and $c$ so that $(a\cdot b)^c$ is not equal to $a^c \cdot b^c$

Set theory ordinals problem Prove that if $b$ is a limit ordinal and $a<b$ then $a+b=b$ (a is any ordinal number)

Suggestion for a textbook including Von Neumann definition of ordinal numbers

Do we need Axiom of Regularity to prove that $a=\{x,\{x\}\}\text{ is an ordinal }\implies x=\emptyset$?

Let $X$ be a non-empty set of ordinals. What are the necessary and sufficient conditions for $X$ to be an ordinal?

For any two ordinals $x$ and $y$, either $x\in y$, or $x=y$, or $y\in x$

Double induction on ordinals (If $\ \alpha+1=\beta+1$ then $\alpha=\beta$)

isomorphism from well ordered set to ordinal

Union of a set of ordinals

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