Proofs and Computations (Hardcover)

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 Godel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to PI11-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 PI11-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.

General

Imprint:	Cambridge UniversityPress
Country of origin:	United Kingdom
Series:	Perspectives in Logic
Release date:	December 2011
First published:	December 2011
Authors:	Helmut Schwichtenberg • Stanley S. Wainer
Dimensions:	236 x 160 x 30mm (L x W x T)
Format:	Hardcover
Pages:	480
ISBN-13:	978-0-521-51769-0
Categories:	Books > Science & Mathematics > Mathematics > Mathematical foundations > Mathematical logic
LSN:	0-521-51769-9
Barcode:	9780521517690

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