Annals of Pure and Applied Logic 68 (2):181-224 (1994)

Michael Rathjen
University of Leeds
The paper contains proof-theoretic investigation on extensions of Kripke-Platek set theory, KP, which accommodate first-order reflection. Ordinal analyses for such theories are obtained by devising cut elimination procedures for infinitary calculi of ramified set theory with Пn reflection rules. This leads to consistency proofs for the theories KP+Пn reflection using a small amount of arithmetic and the well-foundedness of a certain ordinal system with respect to primitive decending sequences. Regarding future work, we intend to avail ourselves of these new cut elimination techniques to attain an ordinal analysis of П12 comprehension by approaching П12 comprehension through transfinite levels of reflection.
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DOI 10.1016/0168-0072(94)90074-4
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References found in this work BETA

Proof-Theoretic Analysis of KPM.Michael Rathjen - 1991 - Archive for Mathematical Logic 30 (5-6):377-403.
Notation Systems for Infinitary Derivations.Wilfried Buchholz - 1991 - Archive for Mathematical Logic 30 (5-6):277-296.
Ordinal Notations Based on a Weakly Mahlo Cardinal.Michael Rathjen - 1990 - Archive for Mathematical Logic 29 (4):249-263.
Proof Theory and Ordinal Analysis.W. Pohlers - 1991 - Archive for Mathematical Logic 30 (5-6):311-376.

View all 9 references / Add more references

Citations of this work BETA

An Ordinal Analysis of Parameter Free Π1 2-Comprehension.Michael Rathjen - 2004 - Archive for Mathematical Logic 44 (3):263-362.
Deflationism Beyond Arithmetic.Kentaro Fujimoto - 2019 - Synthese 196 (3):1045-1069.
An Ordinal Analysis of Stability.Michael Rathjen - 2004 - Archive for Mathematical Logic 44 (1):1-62.

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