Question

Countable ordinals having a certain property

score 194 · Answer 1 · 2024-02-09 17:03:11

194

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Countable ordinals having a certain property

Published on 09 Feb 2024 - 17:03

score 63 · Answer 2 · 2024-02-09 18:30:15

63

Views

Proving $\alpha\subset\beta\implies\alpha\in\beta$ for ordinals $\alpha$ and $\beta$

Published on 09 Feb 2024 - 18:30

score 73 · Answer 3 · 2024-02-09 20:18:24

73

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Stuck on Jech's Set Theory Exercise 2.3

Published on 09 Feb 2024 - 20:18

score 97 · Answer 4 · 2024-02-14 22:44:15

97

Views

Taking the limit beyond infinity, with the ordinals

Published on 14 Feb 2024 - 22:44

score 181 · Answer 5 · 2024-02-15 09:59:09

181

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$\varepsilon_0 !$ (ordinal factorial)

Published on 15 Feb 2024 - 9:59

score 75 · Answer 6 · 2024-02-18 12:21:50

75

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How can different representations of the same integer be equivalent?

Published on 18 Feb 2024 - 12:21

score 80 · Answer 7 · 2024-02-20 16:38:24

80

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What is $\epsilon_0 \cdot \omega$?

Published on 20 Feb 2024 - 16:38

score 57 · Answer 8 · 2024-02-23 04:41:23

57

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A countable ordinal which is $\Sigma_n$-definable in first-order ZFC, but not $\Sigma_m^1$-definable in full second-order arithmetic

Published on 23 Feb 2024 - 4:41

score 111 · Answer 9 · 2024-02-26 01:53:37

111

Views

$\omega$-th or $(\omega + 1)$-th when putting odd numbers after even numbers?

Published on 26 Feb 2024 - 1:53

score 67 · Answer 10 · 2026-03-29 05:44:12

67

Views

An ordinal $\nu$ is a natural iff there is no injection $f$ of $\nu$ into $X$ in $\mathscr P(\nu)\setminus\{\nu\}$.

Published on 29 Mar 2026 - 5:44

score 69 · Answer 11 · 2026-03-26 22:19:17

69

Views

Reference request: monoids on ordinal numbers

Published on 26 Mar 2026 - 22:19

score 62 · Answer 12 · 2024-03-13 17:13:04

62

Views

Is possibile to define an exponentiation with respect an ordinal operation?

Published on 13 Mar 2024 - 17:13

score 99 · Answer 13 · 2026-03-27 12:08:02

99

Views

Proving the Weak Goodstein Theorem within $\mathsf{PA}$

Published on 27 Mar 2026 - 12:08

score 101 · Answer 14 · 2026-03-25 11:08:41

101

Views

Transfinite recursion to construct a function on ordinals

Published on 25 Mar 2026 - 11:08

score 74 · Answer 15 · 2024-03-22 13:02:23

74

Views

Finding the first term of a Goodstein sequence whose expression has maximum exponent

Published on 22 Mar 2024 - 13:02

List Question

Countable ordinals having a certain property

Proving $\alpha\subset\beta\implies\alpha\in\beta$ for ordinals $\alpha$ and $\beta$

Stuck on Jech's Set Theory Exercise 2.3

Taking the limit beyond infinity, with the ordinals

$\varepsilon_0 !$ (ordinal factorial)

How can different representations of the same integer be equivalent?

What is $\epsilon_0 \cdot \omega$?

A countable ordinal which is $\Sigma_n$-definable in first-order ZFC, but not $\Sigma_m^1$-definable in full second-order arithmetic

$\omega$-th or $(\omega + 1)$-th when putting odd numbers after even numbers?

An ordinal $\nu$ is a natural iff there is no injection $f$ of $\nu$ into $X$ in $\mathscr P(\nu)\setminus\{\nu\}$.

Reference request: monoids on ordinal numbers

Is possibile to define an exponentiation with respect an ordinal operation?

Proving the Weak Goodstein Theorem within $\mathsf{PA}$

Transfinite recursion to construct a function on ordinals

Finding the first term of a Goodstein sequence whose expression has maximum exponent

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