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Subsystems of Second Order Arithmetic

Subsystems of Second Order Arithmetic

Subsystems of Second Order Arithmetic
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Subsystems of Second Order Arithmetic Hardback - 2009

by Simpson, Stephen G

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Cambridge Univ Pr, 2009. Hardcover. New. 2nd edition. 460 pages. 9.10x6.30x1.20 inches.
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Details

  • Title Subsystems of Second Order Arithmetic
  • Author Simpson, Stephen G
  • Binding Hardback
  • Edition First Edition
  • Condition New
  • Pages 464
  • Volumes 1
  • Language ENG
  • Publisher Cambridge Univ Pr, Cambridge
  • Publication date 2009
  • Features Bibliography, Index, Table of Contents
  • Bookseller's Inventory # x-052188439X
  • ISBN 9780521884396 / 052188439X
  • Weight 1.65 lbs (0.75 kg)
  • Dimensions 9.3 x 6.2 x 1.2 in (23.62 x 15.75 x 3.05 cm)
  • Category Mathematics
  • Library of Congress subjects Predicate calculus
  • Library of Congress Catalogue Number 2008052364
  • Dewey Decimal Code 511.3
  • Quantity available 2

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Reader reviews for Subsystems of Second Order Arithmetic

From the publisher

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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