Advances in Proof Theory
Editors: Kahle, Reinhard, Strahm, Thomas, Studer, Thomas (Eds.)
Free Preview- 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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- About this book
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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)
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A Survey on Ordinal Notations Around the Bachmann-Howard Ordinal
Pages 1-29
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About Truth and Types
Pages 31-64
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Lindenbaum’s Lemma via Open Induction
Pages 65-77
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Ordinal Analysis of Intuitionistic Power and Exponentiation Kripke Platek Set Theory
Pages 79-172
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Machine-Checked Proof-Theory for Propositional Modal Logics
Pages 173-243
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Table of contents (13 chapters)
- Download Preface 1 PDF (53.8 KB)
- Download Sample pages 2 PDF (323.8 KB)
- Download Table of contents PDF (50.9 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Advances in Proof Theory
- Editors
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- 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
- Softcover ISBN
- 978-3-319-80513-9
- Series ISSN
- 2297-0576
- Edition Number
- 1
- Number of Pages
- XII, 425
- Number of Illustrations
- 10 b/w illustrations
- Topics
