Handbook of Proof Theory

by S.R. Buss (Editor)

Overview

This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.

The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

Product Details

ISBN-13:	9780080533186
Publisher:	Elsevier Science
Publication date:	07/09/1998
Series:	ISSN , #137
Sold by:	Barnes & Noble
Format:	eBook
Pages:	810
File size:	16 MB
Note:	This product may take a few minutes to download.

Table of Contents

Preface. List of Contributors. Chapter I. An Introduction to Proof Theory (S.R. Buss). Chapter II. First-Order Proof Theory of Arithmetic (S.R. Buss). Chapter III. Hierarchies of Provably Recursive Functions (M. Fairtlough, S.S. Wainer). Chapter IV. Subsystems of Set Theory and Second Order Number Theory (W. Pohlers). Chapter V. Gödel's Functional ("Dialectica") Interpretation (J. Avigad, S. Feferman). Chapter VI. Realizability (A.S. Troelstra). Chapter VII. The Logic of Provability (G. Japaridze, D. de Jongh). Chapter VIII. The Lengths of Proofs (P. Pudl´k). Chapter IX. A Proof-Theoretic Framework for Logic Programming (G. Jäger, R.F. Stärk). Chapter X. Types in Logic, Mathematics and Programming (R.L. Constable). Name Index. Subject Index.

Editorial Reviews

These ten articles covering a broad spectrum of the mathematical aspects of the study of proofs as formal objects should be of interest to a diverse audience beyond specialists in the field including logicians, computer scientists, and philosophers. Chapters by 13 contributors provide in-depth coverage of selected topics in proof theory. Articles by the editor provide an introduction, with some subsequent chapters derived from core classical areas (e.g. Avigad and Feferman on Godel's functional interpretation), and others focusing on subjects relevant to computer science (e.g. Constable's types in logic, mathematics, and programming). May be considered a successor to the proof theory portion of the 1977 Handbook of Mathematical Logic (Barwise, ed., Elsevier Science). Annotation c. by Book News, Inc., Portland, Or.

Booknews

Toshiyasu Arai
"The Handbook is most welcome in the logic community. I recommend the Handbook to researchers and graduate students in logic, mathematics, computer science, philosophy, linguistics, artificial intelligence, automated reasoning and cognitive sciences." —Bulletin of Symbolic Logic

From the Publisher