A Buchholz Derivation System for the Ordinal Analysis of KP + Π₃-Reflection

Journal of Symbolic Logic 71 (4):1237 - 1283 (2006)
Abstract
In this paper we introduce a notation system for the infinitary derivations occurring in the ordinal analysis of KP + Π₃-Reflection due to Michael Rathjen. This allows a finitary ordinal analysis of KP + Π₃-Reflection. The method used is an extension of techniques developed by Wilfried Buchholz, namely operator controlled notation systems for RS∞-derivations. Similarly to Buchholz we obtain a characterisation of the provably recursive functions of KP + Π₃-Reflection as <-recursive functions where < is the ordering on Rathjen's ordinal notation system J(K). Further we show a conservation result for $\Pi _{2}^{0}$-sentences
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DOI 10.2178/jsl/1164060454
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References found in this work BETA
Proof Theory of Reflection.Michael Rathjen - 1994 - Annals of Pure and Applied Logic 68 (2):181-224.
Proof Theory for Theories of Ordinals—I: Recursively Mahlo Ordinals.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 122 (1-3):1-85.
Proof Theory for Theories of Ordinals II: Π3-Reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1-3):39-92.
An Ordinal Analysis of Stability.Michael Rathjen - 2004 - Archive for Mathematical Logic 44 (1):1-62.

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