Subsystems of Second Order Arithmetic
By: by Stephen G. Simpson
Series: Perspectives in Mathematical Logic; Perspectives in mathematical logic
Publisher: Springer Berlin Heidelberg
Published: 1999
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 444
ISBN-13: 9783642642036; 9783642599712
Subjects: Mathematics; Symbolic and mathematical Logic; Computer science
Description: "From the point of view of the foundations of mathematics, this definitive work by Simpson is the most anxiously awaited monograph for over a decade. The "subsystems of second order arithmetic" provide the basic formal systems normally used in our current understanding of the logical structure of classical mathematics. Simpson provides an encyclopedic treatment of these systems with an emphasis on *Hilbert's program* (where infinitary mathematics is to be secured or reinterpreted by finitary mathematics), and the emerging *reverse mathematics* (where axioms necessary for providing theorems are determined by deriving axioms from theorems). The classical mathematical topics treated in these axiomatic terms are very diverse, and include standard topics in complete separable metric spaces and Banach spaces, countable groups, rings, fields, and vector spaces, ordinary differential equations, fixed points, infinite games, Ramsey theory, and many others. The material, with its many open problems and detailed references to the literature, is particularly valuable for proof theorists and recursion theorists. The book is both suitable for the beginning graduate student in mathematical logic, and encyclopedic for the expert." Harvey Friedman, Ohio State University.
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Table of contents: title: Preface; title: Acknowledgements; title: Table of Contents; title: Introduction; title: Part A. Development of Mathematics Within Subsystems; title: Recursive Comprehension; title: Arithmetical Comprehension.-Weak König's Lemma; title: Arithmetical Transfinite Recursion; title: Comprehension; title: Part B. Models of Subsystems of Z2; title: Beta-Models; title: Omega-Models; title: Non-Omega-Models; title: Appendix; title: Additional Results; title: Bibliography; title: Index; title: List of Tables. (For detailed Contents, see Contents Internet).