The Joy of Sets: Fundamentals of Contemporary Set Theory

Keith J. Devlin

This text discusses the present aspects of set theory that apply to various subfields of pure mathematics. It begins with a summary of the “naive” set theory, then moves on to the development of the Zermelo-Fraenkel axioms of the theory, and finally moves on to a discussion of ordinal and cardinal numbers. It then gets into modern set theory, discussing issues like the Borel hierarchy and the Lebesgue measure, among others. The concluding chapter presents an alternative view of set theory that applies to computer science.