عنوان

Subsystems of Second Order Arithmetic

(Number (ISBN

3642599710

(Number (ISBN

3642642039

(Number (ISBN

9783642599712

(Number (ISBN

9783642642036

Number

b551218

Title Proper

Subsystems of Second Order Arithmetic

General Material Designation

[Book]

First Statement of Responsibility

by Stephen G. Simpson.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

1999

Specific Material Designation and Extent of Item

(xiv, 444 pages).

Series Title

Perspectives in mathematical logic.

Text of Note

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).

Text of Note

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.

Class number

Book number

by Stephen G. Simpson.

Stephen G Simpson

Electronic name

[Book]

Y