Question

Is Goodstein's theorem equivalent to $\varepsilon_0$-induction over weak base theories (e.g. PRA)?

score 148 · Answer 1 · 2020-07-14 14:25:14

148

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Is Goodstein's theorem equivalent to $\varepsilon_0$-induction over weak base theories (e.g. PRA)?

Published on 14 Jul 2020 - 14:25

score 506 · Answer 2 · 2016-10-19 21:03:04

506

Views

proof theoretic ordinal for Robinson's arithmetic

Published on 19 Oct 2016 - 21:03

score 195 · Answer 3 · 2017-02-26 16:42:04

195

Views

Has the proof theoretic ordinal of $MLTT + M$ been studied?

Published on 26 Feb 2017 - 16:42

score 273 · Answer 4 · 2023-02-21 17:08:05

273

Views

What is an example of a statement equivalent to $\omega^{\omega}$-induction?

Published on 21 Feb 2023 - 17:08

score 84 · Answer 5 · 2023-03-22 09:16:33

84

Views

When should one use transfinite induction?

Published on 22 Mar 2023 - 9:16

score 198 · Answer 6 · 2023-03-31 22:12:17

198

Views

What are the proof-theoretic strengths of Ramsey's theorems?

Published on 31 Mar 2023 - 22:12

score 105 · Answer 7 · 2023-04-01 13:13:33

105

Views

What is the proof theoretic ordinal of $\mathsf{B\Sigma}_{2}^{0}$?

Published on 01 Apr 2023 - 13:13

score 254 · Answer 8 · 2023-06-15 01:18:23

254

Views

What, precisely, does it mean to represent an ordinal on a computer?

Published on 15 Jun 2023 - 1:18

score 267 · Answer 9 · 2023-07-09 13:41:48

267

Views

What is the least upper bound ordinal of my linear n-symbol partition ordinal (ordinal that contain all finite string of finite different symbol)?

Published on 09 Jul 2023 - 13:41

score 72 · Answer 10 · 2023-08-19 06:27:01

72

Views

Is there a model of KP with no $\emptyset'$ ordinal notation for the Bachmann-Howard ordinal?

Published on 19 Aug 2023 - 6:27

score 124 · Answer 11 · 2023-09-28 20:09:40

124

Views

Why do we define the proof-theoretic ordinal of a theory the way we do when there are unnatural well-orderings out there?

Published on 28 Sep 2023 - 20:09

score 60 · Answer 12 · 2023-10-05 00:40:46

60

Views

How large is $f_{\Gamma_{0}}(2)$ in the Fast-Growing Hierarchy?

Published on 05 Oct 2023 - 0:40

score 81 · Answer 13 · 2026-03-24 23:56:08

81

Views

Are finitist systems the ones with a proof-theoretic ordinal of at most $\omega^\omega$?

Published on 24 Mar 2026 - 23:56

score 559 · Answer 14 · 2017-06-24 13:03:41

559

Views

Small proof-theoretic ordinals

Published on 24 Jun 2017 - 13:03

score 111 · Answer 15 · 2017-09-17 09:15:42

111

Views

How is the minimum ordinal to reach TRUE ARITHMETIC starting from PA?

Published on 17 Sep 2017 - 9:15

List Question

Is Goodstein's theorem equivalent to $\varepsilon_0$-induction over weak base theories (e.g. PRA)?

proof theoretic ordinal for Robinson's arithmetic

Has the proof theoretic ordinal of $MLTT + M$ been studied?

What is an example of a statement equivalent to $\omega^{\omega}$-induction?

When should one use transfinite induction?

What are the proof-theoretic strengths of Ramsey's theorems?

What is the proof theoretic ordinal of $\mathsf{B\Sigma}_{2}^{0}$?

What, precisely, does it mean to represent an ordinal on a computer?

What is the least upper bound ordinal of my linear n-symbol partition ordinal (ordinal that contain all finite string of finite different symbol)?

Is there a model of KP with no $\emptyset'$ ordinal notation for the Bachmann-Howard ordinal?

Why do we define the proof-theoretic ordinal of a theory the way we do when there are unnatural well-orderings out there?

How large is $f_{\Gamma_{0}}(2)$ in the Fast-Growing Hierarchy?

Are finitist systems the ones with a proof-theoretic ordinal of at most $\omega^\omega$?

Small proof-theoretic ordinals

How is the minimum ordinal to reach TRUE ARITHMETIC starting from PA?

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