Proof Theory: An Introduction (Lecture Notes in Mathematics, 1407)

Pohlers, Wolfram; Pohlers

ISBN 10: 3540518428 / ISBN 13: 9783540518426

Published by Springer (edition ), 1989

About this Item

The item might be beaten up but readable. May contain markings or highlighting, as well as stains, bent corners, or any other major defect, but the text is not obscured in any way.

Seller Inventory # 3540518428-7-1

Bibliographic Details

• Title: Proof Theory: An Introduction (Lecture Notes in Mathematics, 1407)
• Publisher: Springer (edition )
• Publication Date: 1989
• Language: English
• ISBN 10: 3540518428
• ISBN 13: 9783540518426
• Binding: Paperback
• Condition: Fair

About this title

Synopsis

Although this is an introductory text on proof theory, most of its contents is not found in a unified form elsewhere in the literature, except at a very advanced level. The heart of the book is the ordinal analysis of axiom systems, with particular emphasis on that of the impredicative theory of elementary inductive definitions on the natural numbers. The "constructive" consequences of ordinal analysis are sketched out in the epilogue. The book provides a self-contained treatment assuming no prior knowledge of proof theory and almost none of logic. The author has, moreover, endeavoured not to use the "cabal language" of proof theory, but only a language familiar to most readers.

Review

From the reviews:

"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)

"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 (heuristic accounts of sets, ordinals, logic, etc.), and going into a sophisticated area (impredicativity). ... The author’s main tool is enquiry into truth complexity and ordinal analysis.” (M. Yasuhara, Mathematical Reviews, Issue 2010 a)