Subsystems of Second Order Arithmetic: Second Edition - Couverture souple

Simpson, Stephen G.

Couverture souple

ISBN 10 : 0521150140 ISBN 13 : 9780521150149

Editeur : Cambridge University Press, 2010

Synopsis

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.

A propos du livre

Biographie de l'auteur

Stephen G. Simpson is a mathematician and professor at Pennsylvania State University. The winner of the Grove Award for Interdisciplinary Research Initiation, Simpson specializes in research involving mathematical logic, foundations of mathematics, and combinatorics.

Détails de l'édition

• Éditeur: Cambridge University Press
• Date d'édition: 2010
• ISBN 10: 0521150140
• ISBN 13: 9780521150149
• Reliure: Broché
• Langue: anglais
• Numéro d'édition: 2
• Nombre de pages: 464
• Coordonnées du fabricant: non disponible