Subsystems of Second Order Arithmetic (Hardcover)

Stephen G. Simpson

ISBN 10: 052188439X / ISBN 13: 9780521884396

Editore: Cambridge University Press, Cambridge, 2009

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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 multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9780521884396

Dati bibliografici

• Titolo: Subsystems of Second Order Arithmetic (Hardcover)
• Editore: Cambridge University Press, Cambridge
• Data di pubblicazione: 2009
• Lingua: Inglese
• ISBN 10: 052188439X
• ISBN 13: 9780521884396
• Rilegatura: Hardcover
• Edizione: seconda edizione
• Condizione: new

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Riassunto

Through a series of case studies, this volume examines these axioms to prove particular theorems in core mathematical areas.

Informazioni sull?autore

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.