Proof Theory
Proof Theory
Summary
The kernel of this book consists of a series of lectures on in?nitary proof theory which I gave during my time at the Westfalische ¨ Wilhelms–Universitat ¨ in Munster ¨ . 9, a theorem which is very satisfying in itself - though its real importance lies in the ordinal analysis of systems, weaker than those treated here.
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Proof Theory by Wolfram Pohlers
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.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)Wolfram Pohlers (born 1943) is Full Professor and Director of the Institute for Mathematical Logic and Foundational Resarch at the Westfälische Wilhelms-Universität in Münster, Germany. He received his scientific training at the University of Munich where he worked as an Associate Professor from 1980 to 1985. From 1989 to 1990 he was a visiting scholar at the MSRI in Berkley and in 2005 he taught at the Ohio State University in Columbus.
| SKU | Unavailable |
| ISBN 13 | 9783540693185 |
| ISBN 10 | 3540693181 |
| Title | Proof Theory |
| Author | Wolfram Pohlers |
| Series | Universitext |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer |
| Year published | 2008-10-13 |
| Number of pages | 374 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |