Progress in Computer Science and Applied Logic

Advances in Proof Theory

Editors: Kahle, Reinhard, Strahm, Thomas, Studer, Thomas (Eds.)

  • ​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
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eBook $79.99
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  • ISBN 978-3-319-29198-7
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Hardcover $109.00
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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. 

Table of contents (13 chapters)

  • A Survey on Ordinal Notations Around the Bachmann-Howard Ordinal

    Buchholz, Wilfried

    Pages 1-29

  • About Truth and Types

    Cantini, Andrea

    Pages 31-64

  • Lindenbaum’s Lemma via Open Induction

    Ciraulo, Francesco (et al.)

    Pages 65-77

  • Ordinal Analysis of Intuitionistic Power and Exponentiation Kripke Platek Set Theory

    Cook, Jacob (et al.)

    Pages 79-172

  • Machine-Checked Proof-Theory for Propositional Modal Logics

    Dawson, Jeremy E. (et al.)

    Pages 173-243

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-319-29198-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-29196-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Advances in Proof Theory
Editors
  • Reinhard Kahle
  • Thomas Strahm
  • Thomas Studer
Series Title
Progress in Computer Science and Applied Logic
Series Volume
28
Copyright
2016
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-29198-7
DOI
10.1007/978-3-319-29198-7
Hardcover ISBN
978-3-319-29196-3
Series ISSN
2297-0576
Edition Number
1
Number of Pages
XII, 425
Number of Illustrations and Tables
10 b/w illustrations
Topics