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The Foundations of Mathematics in the Theory of Sets : Encyclopedia of Mathematics and Its Applications - John P. Mayberry

The Foundations of Mathematics in the Theory of Sets

Encyclopedia of Mathematics and Its Applications

Paperback

Published: 27th October 2011
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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.

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

Preface
Preliminaries:
The idea of foundations of mathematics
Simple arithmetic
Basic Set Theory:
Semantics, ontology and logic
The principal axioms and definitions of set theory
Cantorian Set Theory:
Cantorian finitism
The axiomatic method
Axiomatic set theory
Euclidean Set Theory:
Euclidian finitism
The Euclidean theory of cardinality
The theory of simply infinite systems
Euclidean set theory from the Cantorian standpoint
Envoi
Appendices
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521172714
ISBN-10: 0521172713
Series: Encyclopedia of Mathematics and Its Applications
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 446
Published: 27th October 2011
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.4 x 15.6  x 2.3
Weight (kg): 0.62