Erschienen: 27.08.2016 Abbildung von Rodin | Axiomatic Method and Category Theory | Softcover reprint of the original 1st ed. 2014 | 2016

Rodin

Axiomatic Method and Category Theory

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106,99 €

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Softcover reprint of the original 1st ed. 2014 2016. Buch. xi, 285 S. 63 s/w-Abbildungen, Bibliographien. Softcover

Springer. ISBN 978-3-319-37551-9

Format (B x L): 15,5 x 23,5 cm

Gewicht: 462 g

In englischer Sprache

Das Werk ist Teil der Reihe: Synthese Library; 364

Produktbeschreibung

This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia.

The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics.

Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences.

This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.

Gesamtwerk

Die 8. Auflage ist wieder auf sechs Bände angelegt. Darin finden sich übersichtlich und in systematischer Gliederung Vertragsmuster aus der Feder erfahrener Experten. Jedem dieser Muster folgen Anmerkungen, mit denen der dem Vertragsentwurf zu Grunde liegende Sachverhalt und die Gründe für die Wahl des spezifischen Formulars erläutert werden.

Autoren

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