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The Legacy of Kurt Schütte

  • Book
  • © 2020

Overview

Editors:
  1. Reinhard Kahle

    1. Departamento de Matemática, Universidade Nova de Lisboa, Caparica, Portugal

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  2. Michael Rathjen

    1. School of Mathematics, University of Leeds, Leeds, UK

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  • Contains contributions by leading experts close to Schütte' s research, that show the enduring influence of his work in modern proof theory
  • The articles range from eye witness accounts of Schütte's scientific life to developments at the current research frontier
  • Includes papers by Schütte himself that have never been published before

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-xix
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  2. History and Memories

    1. Front Matter

      Pages 1-1
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    2. “Sehr geehrter Herr Professor!” Proof Theory in 1949 in a Letter from Schütte to Bernays

      • Reinhard Kahle
      Pages 3-19

    3. Kurt Schütte’s Way

      • Solomon Feferman
      Pages 21-35

    4. … and so on: Schütte on Naming Ordinals

      • John N. Crossley
      Pages 37-46

    5. Kurt Schütte

      • Curt Christian
      Pages 47-52

    6. Memories of Kurt Schütte and the logic group in Munich: A personal report

      • Wolfram Pohlers
      Pages 55-61

    7. Reminiscences of Kurt Schütte

      • Wolfgang Bibel
      Pages 63-69

    8. Mathematische Logik

      • Kurt Schütte, Helmut Schwichtenberg
      Pages 71-91

    9. Remarks on Hilbert’s Proof Theory

      • Kurt Schutte
      Pages 93-98

  3. Proof Theory at Work

    1. Front Matter

      Pages 101-101
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    2. Having a Look Again at Some Theories ofProof-Theoretic Strengths around \( \varGamma_{0} \)

      • Michael Bärtschi, Gerhard Jäger
      Pages 103-128

    3. The Limits of Predicativity Revisited

      • Wolfram Pohlers
      Pages 129-165

    4. A Note on (Meta)predicative Wellordering Proofs

      • Wilfried Buchholz
      Pages 167-170

    5. Well-ordering Principles, ω-models and \( \varPi_{1}^{1} \)-comprehension

      • Michael Rathjen, Ian Alexander Thomson
      Pages 171-215

    6. From Schütte’s Formal Systems to Modern Automated Deduction

      • Wolfgang Bibel, Jens Otten
      Pages 217-251

    7. Calculating Maximal Order Types for Finite Rooted Unstructured Labeled Trees

      • Diana Schmidt, Jeroen van der Meeren, Andreas Weiermann
      Pages 253-264

    8. Cut-Elimination for SBL

      • Toshiyasu Arai
      Pages 265-298

    9. An Upper Bound for the Proof-Theoretic Strength of Martin-Löf Type Theory with W-type and One Universe

      • A. Setzer
      Pages 299-343

    10. Normalization Proof for Derivations in PA after P. Cohen

      • Grigori Mints
      Pages 345-349
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Keywords

About this book

This book on proof theory centers around the legacy of Kurt Schütte and its current impact on the subject. Schütte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schütte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound Γ0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Schütte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts closeto his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Schütte himself that have never been published before.

Editors and Affiliations

  • Departamento de Matemática, Universidade Nova de Lisboa, Caparica, Portugal

    Reinhard Kahle

  • School of Mathematics, University of Leeds, Leeds, UK

    Michael Rathjen

About the editors

Reinhard Kahle is currently the Carl Friedrich von Weizsäcker Professor for Philosophy and History of Science at the University of Tübingen. Before, he was Professor of Mathematics at the University of Coimbra (2003-08) and at the University Nova in Lisbon (2008-18). He is fellow of the Académie Internationale de Philosophie des Sciences. His main research interests include proof theory and the history and philosophy of logic.

Michael Rathjen is currently Professor of Mathematics at Leeds University. He first taught at Münster and the Ohio State University. As a Heisenberg Fellow he worked at several logic research centers, notably OSU, UCLA, Stanford, and Uppsala. In 1996 he joined the University of Leeds. From 2002 till 2006 he was a Professor of Mathematics at the Ohio State University. His research interests include mathematical logic and the philosophy of logic and mathematics.

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