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The Foundations of Mathematics in the Theory of Sets de John P. Mayberry

The Foundations of Mathematics in the Theory of Sets: Encyclopedia of Mathematics and its Applications, cartea 82

Autor John P. Mayberry
en Limba Engleză Paperback – 26 oct 2011
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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  Cambridge University Press – 26 oct 2011 47601 lei  6-8 săpt.
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  Cambridge University Press – 21 mar 2001 87672 lei  6-8 săpt.

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Specificații

ISBN-13: 9780521172714
ISBN-10: 0521172713
Pagini: 446
Dimensiuni: 156 x 234 x 23 mm
Greutate: 0.62 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Encyclopedia of Mathematics and its Applications

Locul publicării:Cambridge, United Kingdom

Cuprins

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.

Recenzii

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

Descriere

This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.