The foundations of mathematics in the theory of sets
 Responsibility
 J.P. Mayberry.
 Imprint
 Cambridge, UK ; New York : Cambridge University Press, 2000.
 Physical description
 xx, 424 p. ; 25 cm.
 Series
 Encyclopedia of mathematics and its applications v. 82
Description
Creators/Contributors
 Author/Creator
 Mayberry, John P.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 415420) and index.
 Contents

 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.
 (source: Nielsen Book Data)
 Publisher's summary

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.
(source: Nielsen Book Data)
Subjects
 Subjects
 Set theory.
Bibliographic information
 Publication date
 2000
 ISBN
 0521770343