Relativized ordinal analysis: The case of Power Kripke–Platek set theory

Annals of Pure and Applied Logic 165 (1):316-339 (2014)
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Abstract

The paper relativizes the method of ordinal analysis developed for Kripke–Platek set theory to theories which have the power set axiom. We show that it is possible to use this technique to extract information about Power Kripke–Platek set theory, KP.As an application it is shown that whenever KP+AC proves a ΠP2 statement then it holds true in the segment Vτ of the von Neumann hierarchy, where τ stands for the Bachmann–Howard ordinal

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10.1016/j.apal.2013.07.016

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Michael Rathjen
University of Leeds

Citations of this work

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References found in this work

Proof-theoretic analysis of KPM.Michael Rathjen - 1991 - Archive for Mathematical Logic 30 (5-6):377-403.
The strength of Mac Lane set theory.A. R. D. Mathias - 2001 - Annals of Pure and Applied Logic 110 (1-3):107-234.
Proof theory of reflection.Michael Rathjen - 1994 - Annals of Pure and Applied Logic 68 (2):181-224.
Countable models of set theories.Harvey Friedman - 1973 - In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York: Springer Verlag. pp. 539--573.
Some applications of Kleene's methods for intuitionistic systems.Harvey Friedman - 1973 - In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York: Springer Verlag. pp. 113--170.

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