Advances in Proof Theory

  • Reinhard Kahle
  • Thomas Strahm
  • Thomas Studer

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Andrea Cantini
    Pages 31-64
  3. Francesco Ciraulo, Davide Rinaldi, Peter Schuster
    Pages 65-77
  4. Jeremy E. Dawson, Rajeev Goré, Jesse Wu
    Pages 173-243
  5. Solomon Feferman
    Pages 269-289
  6. Helmut Schwichtenberg, Monika Seisenberger, Franziskus Wiesnet
    Pages 353-375
  7. Anton Setzer
    Pages 377-408

About this book

Introduction

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. 

Keywords

constructive mathematics ordinal analysis proof search proof theory type theory

Editors and affiliations

  • Reinhard Kahle
    • 1
  • Thomas Strahm
    • 2
  • Thomas Studer
    • 3
  1. 1.Campus de Caparica DM FCTUniv Nova de LisboaCaparicaPortugal
  2. 2.Inst.of Computer Sci. applied math.University of BernBernSwitzerland
  3. 3.Institute of Computer Science and AUniversity of BerneBerneSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-29198-7
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-29196-3
  • Online ISBN 978-3-319-29198-7
  • Series Print ISSN 2297-0576
  • Series Online ISSN 2297-0584
  • About this book