Subsystems of Second Order Arithmetic

Subsystems of Second Order Arithmetic

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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.
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Product details

  • Hardback | 464 pages
  • 157 x 236 x 30mm | 820g
  • Cambridge, United Kingdom
  • English
  • Revised
  • 2nd Revised edition
  • 052188439X
  • 9780521884396
  • 2,663,177

Table of 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 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.
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About Stephen G. Simpson

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.
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