All Questions
Tagged with ordinal-analysis proof-theory
10 questions with no upvoted or accepted answers
9
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Consequences of recent claims of Ordinal Analysis of $Z_2$
Recently Toshiyasu Arai submitted "An ordinal analysis of $\Pi_{N}$-Collection" and Henry Towsner submitted "Proofs that Modify Proofs", both of which claim ordinal analysis of ...
- 161
6
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181
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Iterated $\Pi^1_1$-reflection and non-Gandiness underrepresented in ordinal analyses?
This is a copy of Math StackExchange question #4395977, which I felt was more appropriate for MathOverflow.
Note on terminology: "admissible", "$(^+)$-stable", and "$\Pi^1_1$-...
- 2,031
6
votes
0
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183
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Ordinal strength of iterated truth theories
Consider the theory ${\rm PA}^{\mathbb{T}}$ obtained by adding a truth predicate to Peano arithmetic, applicable to sentences of the unaugmented language and satisfying the compositionality axioms $\...
- 42.8k
6
votes
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421
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What is proof-theoretic ordinal of weak first-order arithmetic?
According to Wikipedia(https://en.wikipedia.org/wiki/Ordinal_analysis) and nlab(https://ncatlab.org/nlab/show/ordinal+analysis), a proof-theoretic ordinal of $\mathsf{PRA}$ is $\omega^\omega$.
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- 178
5
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265
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$Π_2$ strength of KP
I am looking for a characterization of the $Π_2$ statements provable in KP.
Here, KP (often denoted KPω) is the Kripke-Platek set theory, including infinity and full induction on ordinals. Here is ...
- 7,545
4
votes
0
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367
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Ordinal analysis and nonrecursive ordinals
Ordinal analysis is typically described as characterizing recursive ordinals in a theory $T$, but there is a sense in which it can characterize all $T$-ordinals, even those that are nonrecursive.
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- 7,545
3
votes
0
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144
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Partial well-ordering of formulas
Given a theory $T$, for arbitrary formulas $φ$ and $ψ$ that provably in $T$ denote an ordinal, set $[φ]_T < [ψ]_T$ iff provably in $T$, the ordinal denoted by $φ$ is less than the ordinal denoted ...
- 7,545
3
votes
0
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853
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What is the role of the (formalized) omega rule in Ramified Analysis?
In the 1960's, Feferman and Schutte did groundbreaking proof-theoretic work to find out the strength of predicative systems of second-order arithmetic. They used the ramified theory of types, a ...
- 4,587
1
vote
0
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122
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Is there an error in W. Buchholz's paper "A simplified version of local predicativity"?
I want to self-learn proof theory. It seems that the operator controlled derivation method is important in this field, and the paper in the title is the first paper that uses this method.
So I'm ...
- 1,490
0
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157
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How to define BHO alternatives below admissible ordinals?
Bachmann-Howard ordinal is a recursive ordinal. It's not that large compared to those proof-theoretic ordinals of stronger theories, but the definition of BHO is sufficient to illustrate how ...
- 1,490