Proofs and Computations (Perspectives in Logic) - Hardcover

Schwichtenberg, Helmut; Wainer, Stanley S.

Hardcover

ISBN 10: 0521517699 ISBN 13: 9780521517690

Publisher: Cambridge University Press, 2012

Synopsis

Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.

About this title

About the Authors

Helmut Schwichtenberg is an Emeritus Professor of Mathematics at Ludwig-Maximilians-Universität München. He has recently developed the 'proof-assistant' MINLOG, a computer-implemented logic system for proof/program development and extraction of computational content.

Stanley S. Wainer is an Emeritus Professor of Mathematics at the University of Leeds and a past-President of the British Logic Colloquium.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2012
• Language: English
• ISBN 10: 0521517699
• ISBN 13: 9780521517690
• Binding: Hardcover
• Edition number: 1
• Number of pages: 480