Proofs and Computations Hardback
by Helmut (Ludwig-Maximilians-Universitat Munchen) Schwichtenberg, Stanley S. (University of Leeds) Wainer
Part of the Perspectives in Logic series
Hardback
Description
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 Goedel'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.
Information
-
Out of stock
- Format:Hardback
- Pages:480 pages, 8 Line drawings, unspecified
- Publisher:Cambridge University Press
- Publication Date:15/12/2011
- Category:
- ISBN:9780521517690
Information
-
Out of stock
- Format:Hardback
- Pages:480 pages, 8 Line drawings, unspecified
- Publisher:Cambridge University Press
- Publication Date:15/12/2011
- Category:
- ISBN:9780521517690
