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Subsystems of Second Order Arithmetic

2nd Edition

$107.00

Part of Perspectives in Logic

  • Date Published: May 2009
  • availability: Available
  • format: Hardback
  • isbn: 9780521884396

$107.00
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About the Authors
  • Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics, with an eye to the unity of human knowledge. 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. Additional results are presented in an appendix.

    • Includes revised material from the original ASL edition
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    Product details

    • Edition: 2nd Edition
    • Date Published: May 2009
    • format: Hardback
    • isbn: 9780521884396
    • length: 464 pages
    • dimensions: 234 x 156 x 25 mm
    • weight: 0.82kg
    • availability: Available
  • 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.

  • Author

    Stephen G. Simpson, Pennsylvania State University

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