Set Theory 3rd Edition by Thomas Jech (PDF)

Description

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

User’s Reviews

Editorial Reviews: Review 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) 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐As an Encyclopedia covering Set Theory, Math, and Logic, you will be hard pressed to find a better book covering a breadth of standardized topics. These topics form the foundation of applications relating to modern day technologies and methods.However, if you know nothing of Predicate Logic, Set Theory, and Mathematics, this book will leave you hopelessly lost. You need to learning Predicate Logic first. Next, learn basics of Mathematic proofs. Finally, find an introductory text to Set Theory that has an instructional approach to covering ZFC axioms, Ordinal and Cardinal Numbers. Then you will be able to use Jech’s Set Theory text as intended.

⭐Others have already said pretty much everything there is to say about the quality of the content in this book, and as I am still very early in the book myself, I do not have much to say about that. One thing the potential purchaser should be aware of is that many of the proofs leave a good bit of work to the reader, and while this is very beneficial to your overall understanding of the material, it also makes this book a very poor choice to those with little to no experience writing rigorous proofs (although I doubt many beginners are looking to purchase this book anyways).One thing I can definitely attest to is the physical quality of the book. Though I personally think the cover is a bit ugly, the binding is excellent and the printing is very clear. The price may seem a bit steep at first glance, but considering the massive amount of information the book contains and the quality of the printing, it is definitely a good deal.

⭐Brilliant book. I am computer science with a theoretical math degree from 1996. I thought I would get back to abstract math for fun by finally understanding the proof of the independence of the continuum hypothesis. So I got this book and started reading in the middle – Boolean algebras, Model Theory and Forcing. Big mistake, this book can’t be read this way except by experts in the field. So I went to another excellent book, Nick Weaver’s Forcing for Mathematicians and after slowly reading it I largely “have” the proof of independence of CH. Now switched to reading Jech slowly from the beginning and doing some of the exercises. I find it to be of the right level of mathematical rigor to refresh my capacity and appetite for abstract math. It is dense, beautifully written, has a large number of exercises from easy to hard, and overall a most rewarding study.

⭐The mathematical proofs are compactly written for the brevity and for the abstraction. Beautiful.

⭐This book is amazing; an absolute joy to read. It is written in simply perfect mathematical prose: sufficiently terse to be interesting, yet thoroughly accessible to any studying mathematician. If I had to choose a single favorite math book, it would be this one.

⭐This is one of the most complete books in set theory. If you are interested in learning set theory (from the basics to research level) this is a must have book.

⭐I bought it used di , but it is really like new!! ! No one seems to have used it.

⭐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.)

⭐This book is a mammoth survey that covers everything from the basics of set theory to recent research (such as models of set theory involving large cardinals). It is very well written and structured; the proofs are usually easy to follow and there is plenty of informal commentary and some historical notes. The book is in three parts: basic set theory; advanced set theory; and selected topics. Occasionally proofs are omitted or appear in the exercises, which saves space but is not ideal for fostering an understanding of the subject. I would say that the focus of this book is on the use of a technique called forcing to construct models of set theory and to show the independence of various set properties from the standard formalisation of set theory, but there are chapters on combinatorial set theory and descriptive set theory. For an understanding of the basics of forcing other sources have more intuitive motivation: John Burgess’s article in the Handbook of Mathematical Logic is excellent, and I like the treatment in the newly available (2010) reprint of Smullyan and Fitting’s Set Theory and the Continuum Problem. Having said that, for a student of set theory, this is the most comprehensive work that I have come across; and is a valuable reference as well as an enlightening read.

⭐After I studied “Introduction to set theory” by Hrbacek and Jech, I used this book as an undergraduate student to study the more advanced theorems. It’s really well written and it’s generally quite clear. It’s not an introductory book on the argument, but after you have the basic notions it’s really good.

⭐if you’d want to head over to learning the most recent work on set theory… look no more than this voluminous book… you’ve reached a point where climbing this hill would be the most satisfying and rewarding challenge you could’ve ever asked for…

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