Proofs and computations
QA9.54 .S39 2012
- Unknown QA9.54 .S39 2012
- Includes bibliographical references (p. 431-455) and index.
- Preface-- Preliminaries-- Part I. Basic Proof Theory and Computability: 1. Logic-- 2. Recursion theory-- 3. Godel's theorems-- Part II. Provable Recursion in Classical Systems: 4. The provably recursive functions of arithmetic-- 5. Accessible recursive functions, ID<omega and PI11-CA0-- Part III. Constructive Logic and Complexity: 6. Computability in higher types-- 7. Extracting computational content from proofs-- 8. Linear two-sorted arithmetic-- Bibliography-- Index.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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.
(source: Nielsen Book Data)
- Supplemental links
Table of contents only
Contributor biographical information
- Publication date
- Helmut Schwichtenberg, Stanley S. Wainer.
- Perspectives in logic