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 c1 denotes the least nonrecursive ordinal. This paper is self-contained, at least from a technical point of view.
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Dedicated to Kurt Schütte on the occasion of his 80th birthday
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Rathjen, M. Proof-theoretic analysis of KPM. Arch Math Logic 30, 377–403 (1991). https://doi.org/10.1007/BF01621475
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DOI: https://doi.org/10.1007/BF01621475