Subsystems of Second Order Arithmetic Paperback / softback
by Stephen G. (Pennsylvania State University) Simpson
Part of the Perspectives in Logic series
Paperback / softback
Description
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.
Information
-
Out of stock
- Format:Paperback / softback
- Pages:464 pages, Worked examples or Exercises
- Publisher:Cambridge University Press
- Publication Date:18/02/2010
- Category:
- ISBN:9780521150149
Information
-
Out of stock
- Format:Paperback / softback
- Pages:464 pages, Worked examples or Exercises
- Publisher:Cambridge University Press
- Publication Date:18/02/2010
- Category:
- ISBN:9780521150149
