عنوان

Subsystems of Second Order Arithmetic

3642599710

3642642039

9783642599712

9783642642036

b551218

Subsystems of Second Order Arithmetic

[Book]

by Stephen G. Simpson.

Berlin, Heidelberg

Springer Berlin Heidelberg

1999

(xiv, 444 pages).

Perspectives in mathematical logic.

Preface --;Acknowledgements --;Table of Contents --;Introduction --;Part A. Development of Mathematics Within Subsystems --;Recursive Comprehension --;Arithmetical Comprehension.-Weak König's Lemma --;Arithmetical Transfinite Recursion --;Comprehension --;Part B. Models of Subsystems of Z2 --;Beta-Models --;Omega-Models --;Non-Omega-Models --;Appendix --;Additional Results --;Bibliography --;Index --;List of Tables. (For detailed Contents, see Contents Internet).

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.

Computer science.

Logic, Symbolic and mathematical.

Mathematics.

by Stephen G. Simpson.

Stephen G Simpson

[Book]

Y