Collapsing functions based on recursively large ordinals: A well-ordering proof for KPM [Book Review]

Archive for Mathematical Logic 33 (1):35-55 (1994)
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Abstract

It is shown how the strong ordinal notation systems that figure in proof theory and have been previously defined by employing large cardinals, can be developed directly on the basis of their recursively large counterparts. Thereby we provide a completely new approach to well-ordering proofs as will be exemplified by determining the proof-theoretic ordinal of the systemKPM of [R91]

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10.1007/bf01275469

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Michael Rathjen
University of Leeds

Citations of this work

Proof theory of reflection.Michael Rathjen - 1994 - Annals of Pure and Applied Logic 68 (2):181-224.
An ordinal analysis of parameter free Π12-comprehension.Michael Rathjen - 2005 - Archive for Mathematical Logic 44 (3):263-362.

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References found in this work

Proof theory.K. Schütte - 1977 - New York: Springer Verlag.
Admissible Sets and Structures.Jon Barwise - 1978 - Studia Logica 37 (3):297-299.
Proof-theoretic analysis of KPM.Michael Rathjen - 1991 - Archive for Mathematical Logic 30 (5-6):377-403.
A new system of proof-theoretic ordinal functions.W. Buchholz - 1986 - Annals of Pure and Applied Logic 32:195-207.

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