Subsystems of Second Order Arithmetic (9780521150149)

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.

Product details

• Format Paperback | 464 pages
• Dimensions 156 x 234 x 24mm | 640g
• Publication date 18 Feb 2010
• Publisher CAMBRIDGE UNIVERSITY PRESS
• Publication City/Country Cambridge, United Kingdom
• Language English
• Edition Revised
• Edition Statement 2nd Revised edition
• Illustrations note Worked examples or Exercises
• ISBN10 0521150140
• ISBN13 9780521150149
• Bestsellers rank 1,253,983

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