Helmut Schwichtenberg, Stanley S. Wainer

Proofs and Computations

• Gebundenes Buch

Produktbeschreibung

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 ¿11-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 ¿11-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.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 480
• Erscheinungstermin: 28. März 2013
• Englisch
• Abmessung: 240mm x 161mm x 33mm
• Gewicht: 969g
• ISBN-13: 9780521517690
• ISBN-10: 0521517699
• Artikelnr.: 34158405

Autorenporträt

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.