The foundations of mathematics in the theory of sets / J.P. Mayberry

Englisch

Cambridge : Cambridge University Press, 2000. (Original: 2000)

1 Online-Ressource (xx, 424 pages) : digital, PDF file(s).

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Erscheint auch als: Mayberry, John P. *1929-*: The foundations of mathematics in the theory of sets. - Cambridge [u.a.] : Cambridge University Press, 2000. - XX, 424 S

Print version: ISBN 9780521770347

978-1-139-08712-4 : ebook

Weitere Ausgaben: 978-0-521-17271-4 (Druckausgabe) paperback, 978-0-521-77034-7 (Druckausgabe), 978-0-521-77034-7 (Druckausgabe) : hardback, 978-0-521-17271-4 (andere physische Form) : paperback

DOI: 10.1017/CBO9781139087124

Preliminaries -- Idea of foundations for mathematics -- Simple arithmetic -- Basic set theory -- Semantics, ontology, and logic -- Principal axioms and definitions of set theory -- Cantorian set theory -- Cantorian finitism -- Axiomatic method -- Axiomatic set theory -- Euclidean set theory -- Euclidean finitism -- Euclidean theory of cardinality -- Euclidean theory of simply infinite systems -- Euclidean set theory from the cantorian standpoint -- Envoi.

*Mathematik / Grundlage / Mengenlehre

*Set theory

*Set theory

Klassifikation der Library of Congress: QA248

Dewey Dezimal-Klassifikation: 511.3/22

Regensburger Verbund-Klassifikation: SK 150: SA-SP Mathematik / SK Monografien / Mengenlehre und Verbandstheorie, allgemein

Mathematics Subject Classification: *03-02

Mathematics Subject Classification: 00A30

Mathematics Subject Classification: 03A05

Mathematics Subject Classification: 03E30

Mathematics Subject Classification: 03E65

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.

https://zbmath.org/?q=an:0972.03001 [Zentralblatt MATH]

Elektronische Ressource - Nutzung mit Bibliotheksausweis der Staatsbibliothek zu Berlin

Temporär im Bestand der Staatsbibliothek