- Series: Lecture Notes in Computer Science
- Hardcover: 634 pages
- Publisher: Springer-Verlag Telos; 2 Sub edition (January 1997)
- Language: English
- ISBN-10: 3540630481
- ISBN-13: 978-3540630487
- Product Dimensions: 1.8 x 6.5 x 9.8 inches
- Shipping Weight: 2.4 pounds
- Average Customer Review: 9 customer reviews
- Amazon Best Sellers Rank: #17,865,840 in Books (See Top 100 in Books)
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Set Theory (Lecture Notes in Computer Science) 2 Sub Edition
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From the Back Cover
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.--This text refers to an alternate Hardcover edition.
From the reviews of the third edition:
"Thomas Jech’s text has long been considered a classic survey of the state of the set theory … . As every logician will know, this is a work of extraordinary scholarship, essential for any graduate logician who needs to know where the current boundaries of research are situated. Each chapter ends with a valuable historical survey and there is an extensive bibliography. This will continue to be the bible for set theorists in the new century." (Gerry Leversha, The Mathematical Gazette, March, 2005)
"The book does masterly what it is supposed to do. … every mathematician who wishes to refresh his knowledge of set theory will read it with pleasure. … They will also find historical notes, and precise references … . A very comprehensive bibliography, and detailed indexes complete the work. This book fills a serious gap in the literature and there is no doubt that it will become a standard reference … . One can strongly recommend its acquisition for any mathematical library." (Jean-Roger Roisin, Bulletin of the Belgian Mathematical Society, Vol. 11 (3), 2004)
"One of the classical textbooks and reference books in set theory is Jech’s 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 over the last quarter of a century." (Eva Coplakova, Mathematical Reviews, 2004 g)
"Jech’s book, ‘Set Theory’ has been a standard reference for over 25 years. This ‘Third Millennium Edition’, not only includes all the materials in the first two editions, but also covers recent developments of set theory during the last 25 years. We believe that this new version will become a standard reference on set theory for the next few years." (Guohua Wu, New Zealand Mathematical Society Newsletter, April, 2004)
"Jech’s classic monograph has been a standard reference for a generation of set theorists. Though … labeled ‘The Third Millennium Edition’, the present work is in fact a new book. ... Even sections presenting older results have been rewritten and modernized. Exercises have been moved to the end of each section. The bibliography, the section on notation, and the index have been considerably expanded as well. This new edition will certainly become a standard reference on set theory for years to come." (Jörg D. Brendle, Zentralblatt MATH, Vol. 1007, 2003)
"Thomas Jech’s Set Theory contains the most comprehensive treatment of the subject in any one volume. The present third edition is a revised and expanded version … . The third edition has three parts. The first, Jech says, every student of set theory should learn, the second every set theorist should master and the third consists of various results reflecting ‘the state of the art of set theory at the turn of the new millennium’. This last part especially contains a lot of new material." (Martin Bunder, The Australian Mathematical Society Gazette, Vol. 30 (2), 2003)--This text refers to an alternate Hardcover edition.
Top customer reviews
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.)
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.
For the same reason that the book was simply too hard for me, I feel it may be excellent for someone with prior exposure to set theory, and who wants a concise, logically impecable book on the subject.
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.