An ordinal analysis of parameter free Π12-comprehension

Archive for Mathematical Logic 44 (3):263-362 (2005)
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Abstract

Abstract.This paper is the second in a series of three culminating in an ordinal analysis of Π12-comprehension. Its objective is to present an ordinal analysis for the subsystem of second order arithmetic with Δ12-comprehension, bar induction and Π12-comprehension for formulae without set parameters. Couched in terms of Kripke-Platek set theory, KP, the latter system corresponds to KPi augmented by the assertion that there exists a stable ordinal, where KPi is KP with an additional axiom stating that every set is contained in an admissible set.

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10.1007/s00153-004-0232-4

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Michael Rathjen
University of Leeds

Citations of this work

Hilbert's program then and now.Richard Zach - 2002 - In Dale Jacquette, Philosophy of Logic. Malden, Mass.: North Holland. pp. 411–447.
An ordinal analysis of stability.Michael Rathjen - 2005 - Archive for Mathematical Logic 44 (1):1-62.
Well ordering principles and -statements: A pilot study.Anton Freund - 2021 - Journal of Symbolic Logic 86 (2):709-745.
The Bachmann-Howard Structure in Terms of Σ1-Elementarity.Gunnar Wilken - 2006 - Archive for Mathematical Logic 45 (7):807-829.

View all 16 citations / Add more citations

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The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
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Set Theory: An Introduction to Large Cardinals.F. R. Drake & T. J. Jech - 1976 - British Journal for the Philosophy of Science 27 (2):187-191.
Proof theory of reflection.Michael Rathjen - 1994 - Annals of Pure and Applied Logic 68 (2):181-224.

View all 12 references / Add more references