Set Theory

by Thomas J. Jech

Set Theory has experienced a rapid development in recent years, with major advances in forcing, inner models, large cardinals and descriptive set theory. The present book covers each of these areas, giving the reader an understanding of the ideas involved. It can be used for introductory students and is broad and deep enough to bring the reader near the boundaries of current research. Students and researchers in the field will find the book invaluable both as a study material and as a desktop reference.

Genres: Mathematics, Logic, Nonfiction, Science, Textbooks

621 pages, Hardcover

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.