Articles liés à Subsystems of Second Order Arithmetic: Second Edition

Subsystems of Second Order Arithmetic: Second Edition - Couverture souple

Livre 1 sur 17: Perspectives in Logic

Simpson, Stephen G.

 
9780521150149: Subsystems of Second Order Arithmetic: Second Edition
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.

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Présentation de l'éditeur

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.

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2010
Langue
anglais
ISBN 10 
0521150140
ISBN 13 
9780521150149
Reliure
Broché
Numéro d'édition
2
Nombre de pages
464
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

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