Question

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

score 151 · Answer 1 · 2026-04-13 18:18:15

151

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

Published on 13 Apr 2026 - 18:18

score 507 · Answer 2 · 2026-03-25 02:59:34

507

Views

proof theoretic ordinal for Robinson's arithmetic

Published on 25 Mar 2026 - 2:59

score 196 · Answer 3 · 2026-03-25 07:48:31

196

Views

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

Published on 25 Mar 2026 - 7:48

score 274 · Answer 4 · 2026-03-25 03:02:00

274

Views

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

Published on 25 Mar 2026 - 3:02

score 86 · Answer 5 · 2026-03-27 14:45:41

86

Views

When should one use transfinite induction?

Published on 27 Mar 2026 - 14:45

score 199 · Answer 6 · 2026-03-25 06:06:20

199

Views

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

Published on 25 Mar 2026 - 6:06

score 106 · Answer 7 · 2026-03-25 06:03:27

106

Views

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

Published on 25 Mar 2026 - 6:03

score 255 · Answer 8 · 2026-03-25 03:07:17

255

Views

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

Published on 25 Mar 2026 - 3:07

score 268 · Answer 9 · 2026-03-25 03:04:16

268

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 25 Mar 2026 - 3:04

score 73 · Answer 10 · 2026-03-25 03:03:49

73

Views

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

Published on 25 Mar 2026 - 3:03

score 125 · Answer 11 · 2026-03-25 03:04:19

125

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 25 Mar 2026 - 3:04

score 61 · Answer 12 · 2026-03-25 03:07:27

61

Views

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

Published on 25 Mar 2026 - 3:07

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 562 · Answer 14 · 2026-04-10 23:09:17

562

Views

Small proof-theoretic ordinals

Published on 10 Apr 2026 - 23:09

score 112 · Answer 15 · 2026-03-25 03:01:42

112

Views

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

Published on 25 Mar 2026 - 3:01

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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