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The Foundations of Mathematics in the Theory of Sets

Encyclopedia of Mathematics and its Applications

By (author) John P. Mayberry
Format: Paperback / softback
Publisher: Cambridge University Press, Cambridge, United Kingdom
Published: 27th Oct 2011
Dimensions: w 156mm h 234mm d 23mm
Weight: 622g
ISBN-10: 0521172713
ISBN-13: 9780521172714
Barcode No: 9780521172714
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Synopsis
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.

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Review of the hardback: ' ... this book is thought-provoking ... distinctive approach to the twin issues of mathematical ontology and mathematical foundations'. Australasian Journal of Philosophy