Introduction to Modern Set Theory

Introduction to Modern Set Theory is designed for a
one-semester course in set theory at the advanced undergraduate or beginning graduate level. Three features are the full integration into the text of the study of models of set theory, the use of illustrative examples both in the text and in the exercises, and the integration of consistency results and large cardinals into the text early on. This book 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. In particular, great care is taken to develop the intuitions that
lie behind modern, as well as classical, set theory, and to connect set
theory with the rest of mathematics.