Set Theory: A First Course

This undergraduate textbook carefully introduces the fundamentals of axiomatic set theory; a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One can thus say that set theory is a foundation for mathematics. The proofs are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Topics covered include relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers. Exercises are given at the end of each section in a chapter. The second edition includes a new chapter on set-theoretic constructions of the integers, the rational numbers, and the real numbers; a new chapter on models of set theory. There are also new sections on the hyperreals and applications of stationary sets, club sets, and Fodor's Theorem, as well as additional explanation, examples, and figures. A solutions manual is available for instructors.