Format:
1 Online-Ressource (xx, 424 pages)
,
digital, PDF file(s).
ISBN:
9781139087124
Series Statement:
Encyclopedia of mathematics and its applications volume 82
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
,
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.
Additional Edition:
ISBN 9780521172714
Additional Edition:
ISBN 9780521770347
Additional Edition:
ISBN 9780521770347
Additional Edition:
ISBN 9780521172714
Additional Edition:
Erscheint auch als Mayberry, John P., 1929 - 2014 The foundations of mathematics in the theory of sets Cambridge [u.a.] : Cambridge University Press, 2000 ISBN 0521770343
Additional Edition:
Print version ISBN 9780521770347
Language:
English
Subjects:
Mathematics
Keywords:
Mathematik
;
Grundlage
;
Mengenlehre
DOI:
10.1017/CBO9781139087124
URL:
Volltext
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