Journal of Symbolic Logic

A Buchholz derivation system for the ordinal analysis of KP+Π₃-reflection

Markus Michelbrink

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In this paper we introduce a notation system for the infinitary derivations occurring in the ordinal analysis of KP+Π_3-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 𝒯(K). Further we show a conservation result for Π⁰₂-sentences.

Article information

J. Symbolic Logic Volume 71, Issue 4 (2006), 1237-1283.

First available in Project Euclid: 20 November 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03F03, 03F05, 03F07, 03F15, 03F25, 03F35, 03D20

finitary proof theory, ordinal analysis, impredicative theories


Michelbrink, Markus. A Buchholz derivation system for the ordinal analysis of KP +Π₃-reflection. J. Symbolic Logic 71 (2006), no. 4, 1237--1283. doi:10.2178/jsl/1164060454.

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