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Archive for Mathematical Logic

, Volume 30, Issue 5–6, pp 377–403 | Cite as

Proof-theoretic analysis of KPM

  • Michael Rathjen
Article

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.

Keywords

Mathematical Logic Technical Point Notation System Ordinal Notation Cutelimination Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Michael Rathjen
    • 1
  1. 1.Institut für Mathematische Logik und GrundlagenforschungWestfälische Wilhelms-Universität MünsterMünsterFederal Republic of Germany

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