Proof Theory

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.

• Historical Background.- Primitive Recursive Functions and Relations.- Ordinals.- Pure Logic.- Truth Complexity for ?11-Sentences.- Inductive Definitions.- The Ordinal Analysis for PA.- Autonomous Ordinals and the Limits of Predicativity.- Ordinal Analysis of the Theory for Inductive Definitions.- Provably Recursive Functions of NT.- Ordinal Analysis for Kripke–Platek Set Theory with Infinity.- Predicativity Revisited.- Nonmonotone Inductive Definitions.- Epilogue.

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)