Ordinal analysis of non-monotone-definable inductive definitions

Annals of Pure and Applied Logic 156 (1):160-169 (2008)
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Abstract

Exploiting the fact that -definable non-monotone inductive definitions have the same closure ordinal as arbitrary arithmetically definable monotone inductive definitions, we show that the proof theoretic ordinal of an axiomatization of -definable non-monotone inductive definitions coincides with the proof theoretic ordinal of the theory of arithmetically definable monotone inductive definitions

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10.1016/j.apal.2008.06.014

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Wolfram Pohlers
University of Muenster

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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.

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