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December 2006 A Buchholz derivation system for the ordinal analysis of KP+Π₃-reflection
Markus Michelbrink
J. Symbolic Logic 71(4): 1237-1283 (December 2006). DOI: 10.2178/jsl/1164060454

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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Markus Michelbrink. "A Buchholz derivation system for the ordinal analysis of KP+Π₃-reflection." J. Symbolic Logic 71 (4) 1237 - 1283, December 2006. https://doi.org/10.2178/jsl/1164060454

Information

Published: December 2006
First available in Project Euclid: 20 November 2006

zbMATH: 1114.03046
MathSciNet: MR2275858
Digital Object Identifier: 10.2178/jsl/1164060454

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

Keywords: finitary proof theory, ordinal analysis, impredicative theories

Rights: Copyright © 2006 Association for Symbolic Logic

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Vol.71 • No. 4 • December 2006
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