Hardcover. 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. What are the appropriate axioms for mathematics? Through a series of case studies, this volume examines these axioms to prove particular theorems in core areas including 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

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Detalles bibliogr�ficos

T�tulo: Subsystems of Second Order Arithmetic (Hardcover)
Editor: Cambridge University Press, Cambridge
Fecha de publicaci�n: 2009
Idioma: Ingl�s
ISBN 10: 052188439X
ISBN 13: 9780521884396
Encuadernaci�n: Hardcover
Edici�n: 2� Edici�n
Estado: new

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Sinopsis

What are the appropriate axioms for mathematics? Through a series of case studies, this volume examines these axioms to prove particular theorems in core areas including 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.

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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.

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