Question

Proving that $\omega_1$ is a limit ordinal

score 396 · Answer 1 · 2018-06-09 17:43:15

396

Views

Proving that $\omega_1$ is a limit ordinal

Published on 09 Jun 2018 - 17:43

score 401 · Answer 2 · 2018-06-12 02:47:36

401

Views

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

Published on 12 Jun 2018 - 2:47

score 251 · Answer 3 · 2018-06-15 09:19:10

251

Views

How symmetric is the hierarchy of indecomposable ordinals?

Published on 15 Jun 2018 - 9:19

score 163 · Answer 4 · 2018-06-21 20:14:36

163

Views

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

Published on 21 Jun 2018 - 20:14

score 763 · Answer 5 · 2018-06-22 01:31:46

763

Views

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

Published on 22 Jun 2018 - 1:31

score 663 · Answer 6 · 2018-06-23 18:07:57

663

Views

Why do we define ordinals the way we do?

Published on 23 Jun 2018 - 18:07

score 230 · Answer 7 · 2018-06-27 11:24:41

230

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 27 Jun 2018 - 11:24

score 749 · Answer 8 · 2018-06-27 12:47:09

749

Views

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 27 Jun 2018 - 12:47

score 210 · Answer 9 · 2018-07-04 16:48:57

210

Views

Suggestion for a textbook including Von Neumann definition of ordinal numbers

Published on 04 Jul 2018 - 16:48

score 77 · Answer 10 · 2018-07-07 03:44:56

77

Views

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

Published on 07 Jul 2018 - 3:44

score 150 · Answer 11 · 2018-07-08 13:52:28

150

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 08 Jul 2018 - 13:52

score 271 · Answer 12 · 2018-07-09 09:42:29

271

Views

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

Published on 09 Jul 2018 - 9:42

score 93 · Answer 13 · 2018-07-10 12:49:51

93

Views

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

Published on 10 Jul 2018 - 12:49

score 661 · Answer 14 · 2018-07-10 16:51:57

661

Views

isomorphism from well ordered set to ordinal

Published on 10 Jul 2018 - 16:51

score 326 · Answer 15 · 2018-07-14 14:14:03

326

Views

Union of a set of ordinals

Published on 14 Jul 2018 - 14:14

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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