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Advances in Proof Theory

  • Book
  • © 2016

Overview

Editors:
  1. Reinhard Kahle

    1. Campus de Caparica DM FCT, Univ Nova de Lisboa, Caparica, Portugal

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  2. Thomas Strahm

    1. Inst.of Computer Sci. applied math., University of Bern, Bern, Switzerland

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  3. Thomas Studer

    1. Institute of Computer Science and A, University of Berne, Berne, Switzerland

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  • This book contains state-of-the-art contributions to various topics in Proof Theory
  • The papers range from traditional mathematical proof theory via constructive mathematics to applications in computer science
  • This volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years
  • Includes supplementary material: sn.pub/extras

Part of the book series: Progress in Computer Science and Applied Logic (PCS, volume 28)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xii
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  2. A Survey on Ordinal Notations Around the Bachmann-Howard Ordinal

    • Wilfried Buchholz
    Pages 1-29

  3. About Truth and Types

    • Andrea Cantini
    Pages 31-64

  4. Lindenbaum’s Lemma via Open Induction

    • Francesco Ciraulo, Davide Rinaldi, Peter Schuster
    Pages 65-77

  5. Ordinal Analysis of Intuitionistic Power and Exponentiation Kripke Platek Set Theory

    • Jacob Cook, Michael Rathjen
    Pages 79-172

  6. Machine-Checked Proof-Theory for Propositional Modal Logics

    • Jeremy E. Dawson, Rajeev GorĂ©, Jesse Wu
    Pages 173-243

  7. Intuitionistic Decision Procedures Since Gentzen

    • Roy Dyckhoff
    Pages 245-267

  8. The Operational Perspective: Three Routes

    • Solomon Feferman
    Pages 269-289

  9. Some Remarks on the Proof-Theory and the Semantics of Infinitary Modal Logic

    • Pierluigi Minari
    Pages 291-318

  10. From Subsystems of Analysis to Subsystems of Set Theory

    • Wolfram Pohlers
    Pages 319-338

  11. Restricting Initial Sequents: The Trade-Offs Between Identity, Contraction and Cut

    • Peter Schroeder-Heister
    Pages 339-351

  12. Higman’s Lemma and Its Computational Content

    • Helmut Schwichtenberg, Monika Seisenberger, Franziskus Wiesnet
    Pages 353-375

  13. How to Reason Coinductively Informally

    • Anton Setzer
    Pages 377-408

  14. Pointwise Transfinite Induction and a Miniaturized Predicativity

    • Stanley S. Wainer
    Pages 409-425
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Keywords

About this book

The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium “Advances in Proof Theory”, which was held in Bern in December 2013.



​Proof theory came into being in the twenties of the last century, when it was inaugurated by David Hilbert in order to secure the foundations of mathematics. It was substantially influenced by Gödel's famous incompleteness theorems of 1930 and Gentzen's new consistency proof for the axiom system of first order number theory in 1936. Today, proof theory is a well-established branch of mathematical and philosophical logic and one of the pillars of the foundations of mathematics. Proof theory explores constructive and computational aspects of mathematical reasoning; it is particularly suitable for dealing with various questions in computer science. 

Editors and Affiliations

  • Campus de Caparica DM FCT, Univ Nova de Lisboa, Caparica, Portugal

    Reinhard Kahle

  • Inst.of Computer Sci. applied math., University of Bern, Bern, Switzerland

    Thomas Strahm

  • Institute of Computer Science and A, University of Berne, Berne, Switzerland

    Thomas Studer

Bibliographic Information

  • Book Title: Advances in Proof Theory

  • Editors: Reinhard Kahle, Thomas Strahm, Thomas Studer

  • Series Title: Progress in Computer Science and Applied Logic

  • DOI: https://doi.org/10.1007/978-3-319-29198-7

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-29196-3Published: 12 May 2016

  • Softcover ISBN: 978-3-319-80513-9Published: 27 May 2018

  • eBook ISBN: 978-3-319-29198-7Published: 04 May 2016

  • Series ISSN: 2297-0576

  • Series E-ISSN: 2297-0584

  • Edition Number: 1

  • Number of Pages: XII, 425

  • Number of Illustrations: 10 b/w illustrations

  • Topics: Mathematical Logic and Foundations, Logic

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