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Mathematical Proof Theory in the Light of Ordinal Analysis

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Abstract

We give an overview of recent results in ordinal analysis. Therefore,we discuss the different frameworks used in mathematical proof-theory, namely subsystem of analysis including reversemathematics, Kripke–Platek set theory, explicitmathematics, theories of inductive definitions,constructive set theory, and Martin-Löf’s typetheory.

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    Reinhard Kahle

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Kahle, R. Mathematical Proof Theory in the Light of Ordinal Analysis. Synthese 133, 237–255 (2002). https://doi.org/10.1023/A:1020892011851

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