
Subsystems of Second Order Arithmetic
Stephen G. Simpson(Author)
Cambridge University Press
2nd Edition
Published on 18. February 2010
Book
Paperback/Softback
464 pages
978-0-521-15014-9 (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
Target group
Professional and scholarly
Edition type
Revised edition
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 25 mm
Weight
699 gr
ISBN-13
978-0-521-15014-9 (9780521150149)
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Additional editions

Stephen G. Simpson
Subsystems of Second Order Arithmetic
E-Book
09/2009
2nd Edition
Cambridge University Press
€48.99
Available for download
Person
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.