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Results tagged with proof-theory
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user 479330
For question in Proof Theory, where "proofs" themselves are the object of mathematical investigation. It is not to be used to request a proof of some result.
4
votes
0
answers
139
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Part II to Ketonen's "Set Theory for a Small Universe I. The Paris-Harrington Axiom"
There is an unpublished manuscript "Set Theory for a Small Universe I. The Paris-Harrington Axiom" by Ketonen which appeared early in the study of the Paris-Harrington theorem, around 1979. There is a …
- 2,031
3
votes
What is the proof-theoretic ordinal of KPh?
Let $\mathsf{KPh}$ denote the theory $\mathsf{KP}+``\textrm{The recursively inaccessibles are unbounded}\! "$. I haven't found an explicit analysis of $\mathsf{KPh}$ in Rathjen's preprints, but there …
- 2,031
6
votes
0
answers
175
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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 "$\Pi^1_1$-reflecting" can all be fo …
- 2,031
4
votes
Accepted
What are the known large cardinal axioms for which weaker and stronger set theories "catch up"?
Are there cardinal axioms $A$ for which KP+$A$ or CZF+$A$ are as strong as ZFC-(Powerset axiom)+$A$? How about ZF+$A$?
In this answer I am going to treat this as a "know it when you see it" question …
- 2,031
2
votes
Which ordinals can be proof-theoretic ordinals of a reasonable theory?
$\newcommand{\bomega}{\boldsymbol\omega}$Given the definition of bounding ordinal in the post and the potential sensitivity to coding mentioned in edit 2, these seem to be two main ways to formalize b …
- 2,031