ENGLISH

Subsystems of Second Order Arithmetic

By Stephen G. Simpson

Book information

Publisher
Cambridge University Press
Year
2009
ISBN
978-0-521-88439-6, 978-0-511-57985-1
Language
english
Format
PDF
Filesize
2 MB (2041947 bytes)
Series
Perspectives in Logic
Edition
2nd
Pages
462\462
Topic
Mathematics Logic
Library
Kolxo3
Orientation
portrait
Paginated
yes
Scanned
no
Time added
2013-12-29 19:00:00

Description

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

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