Customer Reviews

Set Theory: An Introduction

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This skinny little paperback is supposedly aimed at undergraduate math students looking for their first experience with rigorous set theory. Unfortunately, the book doesn't do a good job of addressing the needs of such an audience.

Instead, the book seems more like a set of instructor's notes for someone *teaching* such a course. The book assumes far too much background knowledge for an introductory text, and its explanations are often just sketches that need to be fleshed out by a skilled instructor.

Another problem with this book is its incomplete bibliography. Rather than include full references, the author just supplies a last name and a date, and refers the reader to the bibliography of some other book -- where the complete reference can be found. Unfortunately, some of these meta-sources are long out of print, so there's no way to follow the reference. Very poor.

There are much better books out there covering the same territory: Enderton is the standard; the introductory text by Hrbacek and Jech is another.

The Geek review was unfair and uninformed. All books are written from the point of view of the background of the author and Robert Vaught was a logician so naturally this introduction to set theory was written from the perspective of a logician and a great one at that. The author places great stress on being intuitive and natural while leaving to the reader things he ought to be able to figure out for himself. The book does require a careful and thoughtful reading but the reward is many insights contained in no other book on this subject. For example, the sections on definition by induction are as clearly written as I have ever seen. This book grabs the replacement axion or principle up front and treats it as obvious as any other axion contrary to the majority of set theory books. As the author says, he leaves well ordering to the last as he finds the proofs related to it more difficult as Cantor himself did. I could go on and on, but to summarize, this book is a goldmine of information on sets and should be revered. Those who think otherwise just aren't up to learning the basics with true understanding. As for the minor point of relying of the index of Frankel for the references, this was standard practice in his day and is a minor flaw.