Synthese

, Volume 133, Issue 1–2, pp 237–255 | Cite as

Mathematical Proof Theory in the Light of Ordinal Analysis

  • Reinhard Kahle
Article

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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© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Reinhard Kahle
    • 1
  1. 1.WSI, Universität TübingenTübingenGermany

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