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Subsystems of Second Order Arithmetic by Stephen G. Simpson
Subsystems of Second Order Arithmetic by Stephen G. Simpson
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Subsystems of Second Order Arithmetic

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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.
Release date Australia
February 18th, 2010
Audience
  • Professional & Vocational
Edition
2nd Revised edition
Illustrations
Worked examples or Exercises
Pages
464
Dimensions
156x234x24
ISBN-13
9780521150149
Product ID
5322014

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