Subsystems of Second Order Arithmetic
2nd Edition
$62.99 ( ) USD
Part of Perspectives in Logic
- Author: Stephen G. Simpson, Pennsylvania State University
- Date Published: September 2009
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
- format: Adobe eBook Reader
- isbn: 9780511577277
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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.
Read more- Includes revised material from the original ASL edition
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×Product details
- Edition: 2nd Edition
- Date Published: September 2009
- format: Adobe eBook Reader
- isbn: 9780511577277
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
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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