Archive for Mathematical Logic

, Volume 30, Issue 5, pp 377–403

Proof-theoretic analysis of KPM

  • Michael Rathjen

DOI: 10.1007/BF01621475

Cite this article as:
Rathjen, M. Arch Math Logic (1991) 30: 377. doi:10.1007/BF01621475


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, whereω1c denotes the least nonrecursive ordinal. This paper is self-contained, at least from a technical point of view.

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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