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Subsystems of Second Order Arithmetic

Name: Subsystems of Second Order Arithmetic
Brand: Cambridge University Press
SKU: 02023959
Price: 27580 HUF
Availability: InStock
Author: Stephen G. Simpson
ISBN: 9780521150149

Stephen G. Simpson

Language

English

Book Paperback

Libristo code: 02023959

Publishers Cambridge University Press, February 2010

Almost all of the problems studied in this book are motivated by an overriding foundational question... Full description

Libristo code: 02023959

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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.