Archive for Mathematical Logic 30 (5-6):377-403 (1991)

Michael Rathjen
University of Leeds
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
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DOI 10.1007/BF01621475
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References found in this work BETA

The Incompleteness Theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of Mathematical Logic. North-Holland. pp. 821 -- 865.
Admissible Sets and Structures.Jon Barwise - 1978 - Studia Logica 37 (3):297-299.
Ordinal Notations Based on a Weakly Mahlo Cardinal.Michael Rathjen - 1990 - Archive for Mathematical Logic 29 (4):249-263.
A New System of Proof-Theoretic Ordinal Functions.W. Buchholz - 1986 - Annals of Pure and Applied Logic 32:195-207.

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Citations of this work BETA

Proof Theory of Reflection.Michael Rathjen - 1994 - Annals of Pure and Applied Logic 68 (2):181-224.
An Ordinal Analysis of Stability.Michael Rathjen - 2005 - Archive for Mathematical Logic 44 (1):1-62.

View all 33 citations / Add more citations

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