The foundations of mathematics in the theory of sets
By: J.P. Mayberry.
Series: Encyclopedia of mathematics and its applications -- v. 82
Publisher: Cambridge University Press
Published: 2000
Place of publication: Cambridge, UK; New York
Language: eng
Number of pages: 424
Subjects: Set theory
Description: 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.
Notes: Includes bibliographical references (p. 415-420) and index.