Question

Exercise from A First Journey through Logic

score 139 · Answer 1 · 2020-09-24 03:25:42

139

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Exercise from A First Journey through Logic

Published on 24 Sep 2020 - 3:25

score 191 · Answer 2 · 2020-09-26 18:01:48

191

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What's the point of ordinal numbers, in particular, large ordinals?

Published on 26 Sep 2020 - 18:01

score 62 · Answer 3 · 2020-10-04 10:47:30

62

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Exist strictly increasing $f \colon \omega _1 \mapsto \mathbb{R}$

Published on 04 Oct 2020 - 10:47

score 179 · Answer 4 · 2026-03-27 14:02:17

179

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Uniqueness of Cantor normal form using powers of 2 in transfinite Nim

Published on 27 Mar 2026 - 14:02

score 181 · Answer 5 · 2026-03-27 22:04:59

181

Views

Absolutely defined ordering on the set of all infinite sequences is not well ordered

Published on 27 Mar 2026 - 22:04

score 65 · Answer 6 · 2020-10-10 02:27:26

Infinite sequences of natural numbers with finite support are equivalent to $\omega^{n_1} c_1 + \omega^{n_2} c_2 + \ldots + \omega^{n_k} c_k$

score 193 · Answer 7 · 2020-10-10 05:15:32

193

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Left subtraction and left division with remainder for ordinals is unique

Published on 10 Oct 2020 - 5:15

score 138 · Answer 8 · 2020-10-13 16:54:25

138

Views

How does $\mathsf{ZF}$ prove the countability of ordinals coming out of functions such as the ordinal collapse function?

Published on 13 Oct 2020 - 16:54

score 109 · Answer 9 · 2026-03-29 15:02:25

109

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Does there exist an Ordinal Turing Machine program which can detect the occurrence of accidentally writable reals on the tape of a simulated program?

Published on 29 Mar 2026 - 15:02

score 261 · Answer 10 · 2020-10-18 11:40:33

261

Views

Intuition behind recursive ordinals and their relationship to ordinal functions

Published on 18 Oct 2020 - 11:40

score 37 · Answer 11 · 2020-10-18 21:40:59

37

Views

Proving Regarding Ordinal Numbers

Published on 18 Oct 2020 - 21:40

score 398 · Answer 12 · 2020-10-19 03:12:26

398

Views

If $\alpha \preceq \beta$ then there is a unique ordinal $\gamma$ such that $\alpha + \gamma = \beta$

Published on 19 Oct 2020 - 3:12

score 324 · Answer 13 · 2020-10-19 19:36:03

324

Views

Willard 17R; uncountably many compact subsets of real line

Published on 19 Oct 2020 - 19:36

score 69 · Answer 14 · 2020-10-21 21:48:33

69

Views

If $A \subset \omega$ and $A \neq \emptyset$ then $\bigcup A=A$ then $A= \omega$

Published on 21 Oct 2020 - 21:48

score 27 · Answer 15 · 2020-10-21 23:17:33

27

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Let $m$ be a cardinal number less than $q$. Prove that a set of cardinality $q$ contains a subset of cardinality $m$.

Published on 21 Oct 2020 - 23:17

List Question

Exercise from A First Journey through Logic

What's the point of ordinal numbers, in particular, large ordinals?

Exist strictly increasing $f \colon \omega _1 \mapsto \mathbb{R}$

Uniqueness of Cantor normal form using powers of 2 in transfinite Nim

Absolutely defined ordering on the set of all infinite sequences is not well ordered

Infinite sequences of natural numbers with finite support are equivalent to $\omega^{n_1} c_1 + \omega^{n_2} c_2 + \ldots + \omega^{n_k} c_k$

Left subtraction and left division with remainder for ordinals is unique

How does $\mathsf{ZF}$ prove the countability of ordinals coming out of functions such as the ordinal collapse function?

Does there exist an Ordinal Turing Machine program which can detect the occurrence of accidentally writable reals on the tape of a simulated program?

Intuition behind recursive ordinals and their relationship to ordinal functions

Proving Regarding Ordinal Numbers

If $\alpha \preceq \beta$ then there is a unique ordinal $\gamma$ such that $\alpha + \gamma = \beta$

Willard 17R; uncountably many compact subsets of real line

If $A \subset \omega$ and $A \neq \emptyset$ then $\bigcup A=A$ then $A= \omega$

Let $m$ be a cardinal number less than $q$. Prove that a set of cardinality $q$ contains a subset of cardinality $m$.

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