Subsystems of Second Order Arithmetic

Stephen G Simpson author

Format:Hardback

Publisher:Cambridge University Press

Published:29th May '09

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Subsystems of Second Order Arithmetic cover

Through a series of case studies, this volume examines these axioms to prove particular theorems in core mathematical areas.

What are the appropriate axioms for mathematics? Through a series of case studies, this volume examines these axioms to prove particular theorems in core areas including 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.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.

ISBN: 9780521884396

Dimensions: 240mm x 160mm x 30mm

Weight: 800g

464 pages

2nd Revised edition