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  1. Home
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  3. Subsystems of Second Order Arithmetic
  • Cited by 384
Publisher:
Cambridge University Press
Online publication date:
February 2010
Print publication year:
2009
Online ISBN:
9780511581007
DOI:
https://doi.org/10.1017/CBO9780511581007
Subjects:
Mathematics, Logic, Categories and Sets, Programming Languages and Applied Logic
Series:
Perspectives in Logic
Information

Book 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.

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