Ordinal analysis by transformations

Annals of Pure and Applied Logic 157 (2-3):269-280 (2009)
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Abstract

The technique of using infinitary rules in an ordinal analysis has been one of the most productive developments in ordinal analysis. Unfortunately, one of the most advanced variants, the Buchholz Ωμ rule, does not apply to systems much stronger than -comprehension. In this paper, we propose a new extension of the Ω rule using game-theoretic quantifiers. We apply this to a system of inductive definitions with at least the strength of a recursively inaccessible ordinal

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Citations of this work

Proof Theory as an Analysis of Impredicativity.Ryota Akiyoshi - 2012 - Journal of the Japan Association for Philosophy of Science 39 (2):93-107.

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References found in this work

Subsystems of set theory and second order number theory.Wolfram Pohlers - 1998 - In Samuel R. Buss (ed.), Handbook of proof theory. New York: Elsevier. pp. 137--209.
Proof theory for theories of ordinals—I: recursively Mahlo ordinals.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 122 (1-3):1-85.
Proof theory for theories of ordinals II: Π3-reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1-3):39-92.

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