John P. Mayberry

Foundations of Mathematics in the Theory of Sets (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 22. März 2001
• Englisch
• ISBN-13: 9781139106467
• Artikelnr.: 52945008

Inhaltsangabe

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.