The Foundations of Mathematics in the Theo...

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Sprache: Englisch

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Beschreibung

This 2001 book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. This leads to an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. The subject matter of the book falls on the borderline between philosophy and mathematics, and should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics.

Inhaltsverzeichnis

Preface; Part I. Preliminaries: 1. The idea of foundations of mathematics; 2. Simple arithmetic; Part II. Basic Set Theory: 3. Semantics, ontology and logic; 4. The principal axioms and definitions of set theory; Part III. Cantorian Set Theory: 5. Cantorian finitism; 6. The axiomatic method; 7. Axiomatic set theory; Part IV. Euclidean Set Theory: 8. Euclidian finitism; 9. The Euclidean theory of cardinality; 10. The theory of simply infinite systems; 11. Euclidean set theory from the Cantorian standpoint; 12. Envoi; Appendices; Bibliography; Index.

Details

Erscheinungsjahr:	2010
Fachbereich:	Grundlagen
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
ISBN-13:	9780521172714
ISBN-10:	0521172713
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Mayberry, John P.
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	234 x 156 x 24 mm
Von/Mit:	John P. Mayberry
Erscheinungsdatum:	07.10.2010
Gewicht:	0,673 kg