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