Subsystems of Second Order Arithmetic (Perspectives in Logic) （2ND）

Simpson, Stephen G.

Cambridge University Press（2010/02発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 464 p.
• 言語 ENG
• 商品コード 9780521150149
• DDC分類 511.3

Full 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.

Contents

List of tables; Preface; Acknowledgements; 1. Introduction; Part I. Development of Mathematics within Subsystems of Z2: 2. Recursive comprehension; 3. Arithmetical comprehension; 4. Weak König's lemma; 5. Arithmetical transfinite recursion; 6. π11 comprehension; Part II. Models of Subsystems of Z2: 7. β-models; 8. ω-models; 9. Non-ω-models; Part III. Appendix: 10. Additional results; Bibliography; Index.