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Proof-theoretic analysis of KPM

Proof-theoretic analysis of KPM KPM is a subsystem of set theory designed to formalize a recursively Mahlo universe of sets. In this paper we show that a certain ordinal notation system is sufficient to measure the proof-theoretic strength ofKPM. This involves a detour through an infinitary calculus RS(M), for which we prove several cutelimination theorems. Full cut-elimination is available for derivations of $$\Sigma (L_{\omega _1^c } )$$ sentences, whereω 1 c denotes the least nonrecursive ordinal. This paper is self-contained, at least from a technical point of view. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Proof-theoretic analysis of KPM

Archive for Mathematical Logic , Volume 30 (6) – Apr 19, 2005

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References (18)

Publisher
Springer Journals
Copyright
Copyright © 1991 by Springer-Verlag
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/BF01621475
Publisher site
See Article on Publisher Site

Abstract

KPM is a subsystem of set theory designed to formalize a recursively Mahlo universe of sets. In this paper we show that a certain ordinal notation system is sufficient to measure the proof-theoretic strength ofKPM. This involves a detour through an infinitary calculus RS(M), for which we prove several cutelimination theorems. Full cut-elimination is available for derivations of $$\Sigma (L_{\omega _1^c } )$$ sentences, whereω 1 c denotes the least nonrecursive ordinal. This paper is self-contained, at least from a technical point of view.

Journal

Archive for Mathematical LogicSpringer Journals

Published: Apr 19, 2005

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