Proofs and computations
 Author/Creator
 Schwichtenberg, Helmut, 1942
 Language
 English.
 Imprint
 Ithaca, NY : Association for Symbolic Logic ; Cambridge : Cambridge University Press, 2012.
 Physical description
 xiii, 465 p. : ill. ; 24 cm.
 Series
 Perspectives in logic.
Access
Available online

Stacks

Unknown
QA9.54 .S39 2012

Unknown
QA9.54 .S39 2012
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Contributors
 Contributor
 Wainer, S. S.
 Association for Symbolic Logic.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 431455) and index.
 Contents

 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 PI11CA0 Part III. Constructive Logic and Complexity: 6. Computability in higher types 7. Extracting computational content from proofs 8. Linear twosorted 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 selfcontained 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 PI11CA0. Ordinal analysis and the (SchwichtenbergWainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and PI11CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover highertype computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a twosorted, highertype arithmetic with linear logic.
(source: Nielsen Book Data)  Supplemental links

Table of contents only
Contributor biographical information
Publisher description
Bibliographic information
 Publication date
 2012
 Responsibility
 Helmut Schwichtenberg, Stanley S. Wainer.
 Series
 Perspectives in logic
 ISBN
 9780521517690
 0521517699