Proof Theory: Second Edition
Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics.
The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.
1001055690
Proof Theory: Second Edition
Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics.
The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.
24.95 In Stock
Proof Theory: Second Edition

Proof Theory: Second Edition

by Gaisi Takeuti
Proof Theory: Second Edition

Proof Theory: Second Edition

by Gaisi Takeuti

Paperback(Second Edition)

$24.95 
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Overview

Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics.
The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.

Product Details

ISBN-13: 9780486490731
Publisher: Dover Publications
Publication date: 02/20/2013
Series: Dover Books on Mathematics
Edition description: Second Edition
Pages: 512
Product dimensions: 5.90(w) x 8.90(h) x 1.20(d)

About the Author

Gaisi Takeuti is Professor Emeritus of Mathematics at the University of Illinois at Urbana-Champaign.

Table of Contents

Preface
Preface to the Second Edition
Contents
Introduction
Part I. First Order Systems
1. First Order Predicate Calculus
2. Peano Arithmetic
Part II. Second Order and Finite Order Systems
3. Second Order Systems and Simple Type Theory
4. Infinitary Logic
Part III. Consistency Problems
5. Consistency Proofs
6. Some Applications of Consistency Proofs
Postscript
Appendix
Index
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