Set Theory (Perspectives in Mathematical Logic) (Hardcover)

~ (Author) "Intuitively, a set is a collection of all elements that satisfy a certain given property..." (more)
Key Phrases: projective stationary, closed unbounded filter, perfect set property, Axiom of Choice, Martin's Axiom, Continuum Hypothesis (more...)

Editorial Reviews

Product Description

This introduction to modern set theory covers all aspects of its two main general areas: classical set theory including large cardinals, infinitary combinatorics, desriptive set theory, and independence proofs starting with Goedel's proof around 1938 followed by Cohen's proof in 1963, whereby Cohen's method of forcing probably had a greater influence on mathematics. The author's primary emphasis is on forcing and large cardinals (on which he has collected an enormous amount of material which had previously been available only through scattered journal articles or private communication) but there is a substantial discussion of descriptive set theory and infinitary combinatorics as well. The author's presentation is very well-organized and carefully worked out and has become a standard reference.

Product Details

• Hardcover: 634 pages
• Publisher: Springer-Verlag Telos; 2nd edition (October 31, 1997)
• Language: English
• ISBN-10: 3540630481
• ISBN-13: 978-3540630487
• Product Dimensions: 9.8 x 6.5 x 1.8 inches
• Shipping Weight: 2.4 pounds
• Average Customer Review: 4.6 out of 5 stars  See all reviews (5 customer reviews)
• Amazon.com Sales Rank: #5,904,455 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

57 of 59 people found the following review helpful:

5.0 out of 5 stars My favorite book on set theory., August 16, 1998

By A Customer

This review is from: Set theory, Volume 79 (Pure and Applied Mathematics) (Hardcover)

In 1979, I was a first-year graduate student in mathematics. One summer day, I was looking in the math section of Stanford bookstore and saw this thick green volume with the simple title Set Theory (by Thomas Jech). I couldn't help pulling the tome off the shelf. I flipped through the pages in awe. This book had everything about mathematics that I had always wanted to know.

After about an hour, I reluctantly looked at the price and it was just too much; I had to put it back on the shelf. But for the next month, that book was all I could think about. I finally went back and bought it.

Two years later after hooking up with my adviser and embarking on research in set theory, I started working through Jech's book starting on page 1. It took me 2 years to work through the entire book, and for much of that time I had the opportunity to present what I was learning in seminars.

That book is a real treasure. I don't think I've spent as much time poring over any other book. I think the presentation of material is fantastic and the coverage is thorough (or it was at the time I studied it--probably his recently updated work also has this attribute).

I would recommend this book (or rather the most recent edition of it) to any serious graduate student specializing in set theory.

Two areas where I needed supplementary study were in his approaches to the constructible universe and to forcing. These are important areas, and Jech does a fine job in his approach, but certain approaches other than his have become more of a standard, and any serious researcher will have to become familiar with these standards. Jech uses Boolean algebras (primarily) in his development of forcing (and his development is excellent) whereas by now, the usual approach is with partial orders. Also, Jech develops L as a transitive model that is closed under "Godel operations"--a perfectly valid approach. These days, though, the formula-based approach is more common in the literature.

Nonetheless, Jech's wide variety of forcing applications, his in-depth treatment of large cardinals, and his compact surveys of saturated ideals and descriptive set theory make his work really an outstanding contribution.

14 of 14 people found the following review helpful:

4.0 out of 5 stars Clear and comprehensive, July 11, 2005

By	Nathan Oakes (Ashland, Oregon) - See all my reviews

This review is from: Set Theory (Hardcover)

The author tried to cover everything a set theorist should master plus a representative selection of topics of current interest. That makes for a lot of ground to cover, but Jech did a great job. The writing is very well organized and clear. Every short chapter has many exercises, often with hints. There are extensive sections on applications of forcing. The indexes are really good.

There has to be a down side, of course. In order to squeeze so much in, he had to be brief. There is little context provided, especially in Part I: Basic Set Theory. There are rarely any examples and only the main facts are covered. That is all part of an understandable compromise, but I have a serious complaint (my only one) about the references. He gives detailed historical references in each chapter, but no references to further reading. He could have done it with hardly any use of space and it would have been very helpful.

Because of the brevity, it is a bit hard to learn from, but it makes a great secondary reference. For example, its explanations are often clearer and more direct than in Kunen and with more detailed proofs. It you are going to have any more exposure to set theory than an introductory course, you will probably want to buy a copy. (BTW, the 2e was just a corrected reprint; 3e is a complete rewrite.)

29 of 33 people found the following review helpful:

5.0 out of 5 stars This edition has been completely revised!, February 12, 2003

By	Steven E. Collins (Austin, TX USA) - See all my reviews (REAL NAME)

This review is from: Set Theory (Hardcover)

Just wanted to point out that all the reviews here dated before Feb 2003 are referring to older editions. The new one has been totally revised (no laundry list of corrections at the end) and also expanded -- lots of material from the last 25 years of set theory research is now included. Most notable among these is material on proper forcing and pcf theory. (There is even a section on my research interest, mutually stationary sets, and this is a notion which was just published for the first time 2 years ago!) The book is still just as informative and readable as the previous editions.

EDIT: I still agree with everything I wrote above; nearly 6 years later, I still read portions of this book almost every day (and I'm not even doing set theory per se professionally anymore). However I should state for the record that the book is RIDDLED with typos and minor errors. So, be prepared to read critically.