Subsystems of Second Order Arithmetic
2nd Edition
Published on 3. September 2009
978-0-511-57727-7 (ISBN)
Description
Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core mathematical areas such as algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics. In many cases, if a mathematical theorem is proved from appropriately weak set existence axioms, then the axioms will be logically equivalent to the theorem. Furthermore, only a few specific set existence axioms arise repeatedly in this context, which in turn correspond to classical foundational programs. This is the theme of reverse mathematics, which dominates the first half of the book. The second part focuses on models of these and other subsystems of second-order arithmetic.
More details
Series
Edition
2nd Revised edition
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Edition type
Revised edition
Illustrations
Worked examples or Exercises
File size
5,92 MB
ISBN-13
978-0-511-57727-7 (9780511577277)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Stephen G. Simpson
Subsystems of Second Order Arithmetic
Book
02/2010
2nd Edition
Cambridge University Press
€72.00
Shipment within 15-20 days
Stephen G. Simpson
Subsystems of Second Order Arithmetic
Book
05/2009
2nd Edition
Cambridge University Press
€194.90
Shipment within 15-20 days
Person
Stephen G. Simpson is a mathematician and professor at Pennsylvania State University. The winner of the Grove Award for Interdisciplinary Research Initiation, Simpson specializes in research involving mathematical logic, foundations of mathematics, and combinatorics.
Content
List of tables; Preface; Acknowledgements; 1. Introduction; Part I. Development of Mathematics within Subsystems of Z2: 2. Recursive comprehension; 3. Arithmetical comprehension; 4. Weak Koenig's lemma; 5. Arithmetical transfinite recursion; 6. ?11 comprehension; Part II. Models of Subsystems of Z2: 7. ?-models; 8. ?-models; 9. Non-?-models; Part III. Appendix: 10. Additional results; Bibliography; Index.
