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Gentzen's Centenary

The Quest for Consistency

  • Reinhard Kahle
  • Michael Rathjen

Table of contents

  1. Front Matter
    Pages i-x
  2. Reflections

    1. Front Matter
      Pages 1-1
    2. Reinhard Kahle
      Pages 3-24
    3. Michael Detlefsen
      Pages 25-44
  3. Gentzen’s Consistency Proofs

  4. Results

    1. Front Matter
      Pages 243-243
    2. Sam Buss
      Pages 245-277
    3. Fernando Ferreira
      Pages 279-300
    4. Herman Ruge Jervell
      Pages 301-315
    5. Wolfram Pohlers
      Pages 317-354
  5. Developments

    1. Front Matter
      Pages 355-355
    2. Michael Rathjen, Pedro Francisco Valencia Vizcaíno
      Pages 533-561

About this book

Introduction

Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory.   

Keywords

Consistency Proof Gentzen Formal Systems Gentzen's Main Theorem Ordinal Analysis Proof Theory

Editors and affiliations

  • Reinhard Kahle
    • 1
  • Michael Rathjen
    • 2
  1. 1.Departamento de Matemática, FCTUniversidade Nova de LisboaLisbonPortugal
  2. 2.School of MathematicsUniversity of LeedsLeedsUnited Kingdom

Bibliographic information