عنوان

Subsystems of Second Order Arithmetic

شابک

3642599710

شابک

3642642039

شابک

9783642599712

شابک

9783642642036

شماره

b551218

عنوان اصلي

Subsystems of Second Order Arithmetic

نام عام مواد

[Book]

نام نخستين پديدآور

by Stephen G. Simpson.

محل نشرو پخش و غیره

Berlin, Heidelberg

نام ناشر، پخش کننده و غيره

Springer Berlin Heidelberg

تاریخ نشرو بخش و غیره

1999

نام خاص و کميت اثر

(xiv, 444 pages).

عنوان فروست

Perspectives in mathematical logic.

متن يادداشت

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).

متن يادداشت

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.

موضوع مستند نشده

Computer science.

موضوع مستند نشده

Logic, Symbolic and mathematical.

موضوع مستند نشده

Mathematics.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

by Stephen G. Simpson.

مستند نام اشخاص تاييد نشده

Stephen G Simpson

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y