, Volume 30, Issue 5-6, pp 377-403

Proof-theoretic analysis of KPM

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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.

Dedicated to Kurt Schütte on the occasion of his 80th birthday