Proof Theory

1. Front Matter

   Pages I-VIII

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2. Introduction

   Pages 1-6

3. Ordinal Analysis of Pure Number Theory

   Pages 7-76

4. The autonomous ordinal of the infinitary system Z∞ and the limits of predicativity

   Pages 77-108

5. Ordinal analysis of the formal theory for noniterated inductive definitions

   Pages 109-186

6. Back Matter

   Pages 187-213

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Although this is an introductory text on proof theory, most of its contents is not found in a unified form elsewhere in the literature, except at a very advanced level. The heart of the book is the ordinal analysis of axiom systems, with particular emphasis on that of the impredicative theory of elementary inductive definitions on the natural numbers. The "constructive" consequences of ordinal analysis are sketched out in the epilogue. The book provides a self-contained treatment assuming no prior knowledge of proof theory and almost none of logic. The author has, moreover, endeavoured not to use the "cabal language" of proof theory, but only a language familiar to most readers.

• calculus
• number theory
• proof
• proof theory

• Institut für Mathematische Logik und Grundlagenforschung, Westfälische Wilhelms-Universität, Münster, Germany

  Wolfram Pohlers

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