Introduction to Modern Set Theory

It is designed for a one-semester course in set theory at the advanced undergraduate or beginning graduate level. It assumes no knowledge of logic, and no knowledge of set theory beyond the vague familiarity with curly brackets, union and intersection usually expected of an advanced mathematics student. It grew out of my experience teaching this material in a first-year graduate course at the University of Kansas over many years. It is aimed at two audiences — students who are interested in studying set theory for its own sake, and students in other areas who may be curious about applications of set theory to their field. While a one-semester course with no logic as a prerequisite cannot begin to tell either group of students all they need to know, it can hope to lay the foundations for further study. In particular, I am concerned with developing the intuitions that lie behind modern, as well as classical, set theory, and with connecting set theory with the rest of mathematics.