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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