Overview

This book verifies with compelling evidence the author's inclination to 'write a book on proof theory which needs no previous knowledge of proof theory'. Avoiding the cryptic terminology of proof as far as possible, the book starts at an elementary level and displays the connections between infinitary proof theory and generalized recursion theory, especially the theory of inductive definitions. As a 'warm up' the classical analysis of Gentzen is presented in a more modern terminology to proceed with explaining and proving the famous result by Feferman and Schutte on the limits of predicativity.The author, too, provides an introduction to ordinal arithmetic, introduces the Veblen hierarchy and employs these functions to design an ordinal notation system for the ordinals below Epsilon 0 and Gamma 0, while emphasizing the first step into impredicativity, i.e., the first step beyond Gamma 0. The earlier version of this book was originally published in 1989 as volume 1407 of the Springer series Lecture Notes in Mathematics .

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9783540865322

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<p>From the reviews: <p> Proof Theory takes various axiom systems that treat induction in different ways and analyzes them from the ordinal viewpoint to gauge their relative strengths. This new version includes several developments in the field that have occurred over the twenty years since the original. Although the current book, appearing in the Universitext series, claims to be pitched at undergraduate/graduate level, an undergraduate course out of Proof theory would be ambitious indeed. (Leon Harkleroad, The Mathematical Association of America, March, 2009)<p> The book is addressed primarily to students of mathematical logic interested in the basics of proof theory, and it can be used both for introductory and advanced courses in proof theory. this book may be recommended to a larger circle of readers interested in proof theory. (Branislav Boricic, Zentrablatt MATH, Vol. 1153, 2009) This is a textbook an excellent one on proof theory, starting from the very elementary (heurist

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