Set Theory: The Third Millennium Edition, revised and expanded

by Thomas J. Jech

This monograph covers the recent major advances in various areas of set theory.

From the reviews:

"One of the classical textbooks and reference books in set theory....The present Third Millennium edition...is a whole new book. In three parts the author offers us what in his view every young set theorist should learn and master....This well-written book promises to influence the next generation of set theorists, much as its predecessor has done." --MATHEMATICAL REVIEWS"

Genres: Mathematics, Logic, Nonfiction, Textbooks, Science

786 pages, Paperback

First published January 1, 1978

Reviews

[Ben · Rating 5 out of 5]

This is easily the best text for the want-to-be set theorist. I will admit it has its flaws, but for such a comprehensive book that's excusable. My suggestions to someone reading Jech:

- If you're learning about constructability/L or forcing for the first time, I would recommend Kunen's book instead. Then you can skip over Jech's treatment of L but his approach to forcing is important to know.

- The section on iterated ultrapowers is the only one that is truly bad. I recommend pretending this section doesn't exist and instead reading the paper "Itreated Ultrapowers" by John Steel. It can be found on his website.

- Don't bother with the proof of Jensen's Covering Lemma in this book. Jech does it in a really strange way and doesn't even finish the proof. In general Schindler's book is much better for learning the fine structure of L.

Despite these few flaws, I think Jech is an amazing book. I highly recommend the rest of the book.

[Yauhen Yakimovich · Rating 5 out of 5]

Pure joy

[Tony Strimple · Rating 4 out of 5]

Stellar coverage of the fundamentals of set theory, albeit a bit verbose. Kunen's succinct treatment, however, is still better overall. Good for a quiet weekend. I'll let you know how the sections on large cardinals pan out.