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Perspectives in Logic Ser.: Proofs and Computations by Helmut Schwichtenberg and Stanley S. Wainer (2011, Hardcover)
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Proofs and Computations, Hardcover by Schwichtenberg, Helmut; Wainer, Stanley S., ISBN 0521517699, ISBN-13 9780521517690, Brand New, Free shipping in the US
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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-100521517699
ISBN-139780521517690
eBay Product ID (ePID)109497126
Product Key Features
Number of Pages480 Pages
Publication NameProofs and Computations
LanguageEnglish
Publication Year2011
SubjectLogic
TypeTextbook
AuthorHelmut Schwichtenberg, Stanley S. Wainer
Subject AreaMathematics
SeriesPerspectives in Logic Ser.
FormatHardcover
Dimensions
Item Height1.2 in
Item Weight30.5 Oz
Item Length9.3 in
Item Width6.3 in
Additional Product Features
Intended AudienceScholarly & Professional
Reviews"Written by two leading practitioners in the area of formal logic, the book provides a panoramic view of the topic. This reference volume is a must for the bookshelf of every practitioner of formal logic and computer science." Prahladavaradan Sampath, Computing Reviews
Dewey Edition23
IllustratedYes
Dewey Decimal511.352
Table Of ContentPreface; 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< and 11-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.
SynopsisDriven 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 G del'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., 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., Written by acknowledged experts, for advanced students and researchers in mathematical logic and computer science, this volume provides a detailed, self-contained coverage of proof theory in both classical and constructive arithmetics, up to finitely iterated inductive definitions. Deep connections with computability, complexity and program extraction form the principal themes.
LC Classification NumberQA9.54 .S39 2012
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