Description

Book Synopsis

What are the appropriate axioms for mathematics? Through a series of case studies, this volume examines these axioms to prove particular theorems in core areas including 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.

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 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.

Subsystems of Second Order Arithmetic

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    A Paperback by Stephen G. Simpson

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      Book details

      Publisher Cambridge University Press
      Published 18 February 2010
      ISBN-13 9780521150149
      978-0521150149
      ISBN-10 0521150140
      Also in:
      Mathematical logic

      Description

      Book Synopsis

      What are the appropriate axioms for mathematics? Through a series of case studies, this volume examines these axioms to prove particular theorems in core areas including 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.

      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 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.

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