Proofs and Computations PDF
by Helmut (Ludwig-Maximilians-Universitat Munchen) Schwichtenberg, Stanley S. (University of Leeds) Wainer
Part of the Perspectives in Logic series
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 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.
Information
-
Download - Immediately Available
- Format:PDF
- Pages:Worked examples or Exercises; 8 Line drawings, unspecified
- Publisher:Cambridge University Press
- Publication Date:06/02/2012
- Category:
- ISBN:9781139210577
Information
-
Download - Immediately Available
- Format:PDF
- Pages:Worked examples or Exercises; 8 Line drawings, unspecified
- Publisher:Cambridge University Press
- Publication Date:06/02/2012
- Category:
- ISBN:9781139210577
