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

Markus Michelbrink
The Journal of Symbolic Logic
Vol. 71, No. 4 (Dec., 2006), pp. 1237-1283
Stable URL: http://www.jstor.org/stable/27588512
Page Count: 47
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A Buchholz Derivation System for the Ordinal Analysis of KP + Π₃-Reflection
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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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