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Subsystems of second order arithmetic /
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 to...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
©2009.
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| Edición: | 2nd ed. |
| Colección: | Perspectives in logic.
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| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | 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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| Notas: | "Association for Symbolic Logic." |
| Descripción Física: | 1 online resource (xvi, 444 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 409-424) and index. |
| ISBN: | 9780511580680 0511580681 9780511579110 051157911X |