# Proof-theoretic analysis of KPM

@article{Rathjen1991ProoftheoreticAO, title={Proof-theoretic analysis of KPM}, author={Michael Rathjen}, journal={Archive for Mathematical Logic}, year={1991}, volume={30}, pages={377-403} }

AbstractKPM 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…

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