Notes on Set Theory (Undergraduate Texts in Mathematics)

Rating:
Summary: A key into the realm of mathematical insanity
Review: I took two courses from Professor Moschovakis which used this book as their text. I highly recommend this book for anyone who has always wanted to learn about set theory. It starts off with Cantor's naive concept on set theory and his proofs concerning the "sizes" of infinite sets. From there, it presents Russell's Paradox, which created the necessity for the axiomatic system that Zermelo developed in 1908. From there, the book discusses the "construction" of the natural numbers, cardinal/ordinal arithmetic, partially and well-ordered sets, the results of the Axioms of Choice and Replacement, and much more. The only thing that I would criticize this book for is that sometimes the theorems that you'd really like to see proofs of are left as homework assignments. Other than that, this book rocks!