Subsystems of Second Order Arithmetic (Perspectives in Logic)

Simpson, Stephen G.

ISBN 10: 0521150140 / ISBN 13: 9780521150149

Published by Cambridge University Press, 2010

About this Item

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Bibliographic Details

• Title: Subsystems of Second Order Arithmetic (Perspectives in Logic)
• Publisher: Cambridge University Press
• Publication Date: 2010
• Language: English
• ISBN 10: 0521150140
• ISBN 13: 9780521150149
• Binding: paperback
• Edition: 2nd Edition
• Condition: Good
• Weight: 27 ounces

About this title

Synopsis

Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics, with an eye to the unity of human knowledge. 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. Additional results are presented in an appendix.

Book Description

What are the appropriate axioms for mathematics? Through a series of case studies, this volumes examines these axioms 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.