A Buchholz derivation system for the ordinal analysis of KP+Π₃-reflection
Markus Michelbrink
Source: J. Symbolic Logic Volume 71, Issue 4
(2006), 1237-1283.
Abstract
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.
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03F03, 03F05, 03F07, 03F15, 03F25, 03F35, 03D20
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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1164060454
Digital Object Identifier: doi:10.2178/jsl/1164060454
Mathematical Reviews number (MathSciNet): MR2275858
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