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This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thoUSnd years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis - finding the "right axioms" to prove fundamental theorems - and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation

Parametre knihy

Zaradenie knihy Knihy po anglicky Mathematics & science Mathematics Mathematical foundations

• Celý názov: Reverse Mathematics
• Autor: John Stillwell
• Jazyk: Angličtina
• Väzba: Pevná
• Počet strán: 200
• EAN: 9780691177175
• ISBN: 9780691177175
• ID: 16229363
• Nakladateľ: Princeton Univers. Press
• Hmotnosť: 490 g
• Rozmery: 240 × 161 × 25 mm
• Dátum vydania: 31. January 2018

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