John Stillwell: Reverse Mathematics

Cover: 9780691196411 | Reverse Mathematics | Proofs from the Inside Out | John Stillwell

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Sprache: Englisch

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Beschreibung

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 thousand 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. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it.

Erscheinungsjahr:	2019
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Taschenbuch
Inhalt:	Kartoniert / Broschiert
ISBN-13:	9780691196411
ISBN-10:	0691196419
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Stillwell, John
Hersteller:	Princeton University Press
Maße:	233 x 154 x 20 mm
Von/Mit:	John Stillwell
Erscheinungsdatum:	24.09.2019
Gewicht:	0,317 kg

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