Subsystems of Second Order Arithmetic by Stephen G Simpson

Subsystems of Second Order Arithmetic by Stephen G Simpson

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.

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.

SKU	Unavailable
ISBN 13	9780521884396
ISBN 10	052188439X
Title	Subsystems of Second Order Arithmetic
Author	Stephen G Simpson
Series	Perspectives In Logic
Condition	Unavailable
Binding Type	Hardback
Publisher	Cambridge University Press
Year published	2009-05-29
Number of pages	464
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.