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Cambridge University Press Subsystems of Second Order Arithmetic: Second Edition: Perspectives in Logic

Name: Subsystems of Second Order Arithmetic: Second Edition: Perspectives in Logic
Brand: Cambridge University Press
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Mathematical Logic

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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.

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Brand: Cambridge University Press
Format: paperback
ASIN: 0521150140
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Foundations > Mathematical Logic
Domain: Amazon UK
Release Date: 18 February 2010
Listed Since: 15 February 2010

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Cambridge University Press Subsystems of Second Order Arithmetic: Second Edition: Perspectives in Logic

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