Reviews (1)

Reviews (4)

A good but unreadable book
It's really a good book for researchers in set theory. But it is NOT an introduction for students who want to know what is set theory. You will feel you are so stupid if you read this book without any set theoretical background. I recommand Kunnen's book for those people who are interested in set theory but have no any (or only a little) set theory knowledge.

This edition has been completely revised!
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.

Reviews (6)

The essential essence of set theory in 100 pages
This book is an excellent primer on the basics of set theory that all graduate students need, but are not necessarily obtained in the general undergraduate curriculum. Halmos writes in an abbreviated, yet effective style that imparts the necessary details without an excess of words. Theorems and exercises are very few, so it really cannot be used as a textbook. If you need a great deal of explanations, then it is not for you. However, if your need is for a book that distills the essence of set theory down to the shortest possible size, then this book should be yours, either in your college or personal library.

Mercy Sought
My previous review of Halmos' book stands.Exceptional book, but ... As an example of a question in the book to whet some appetites and in seeking someone's kind mercy in actually answering it for me and putting me out of my misery, consider p.59 on the Axiom of Choice. Quote: if {X (sub)i} is a finite sequence of sets, for i in n say, then a necessary and sufficient condition that their Cartesian product be empty is that at least one of them be empty ... (The case n=0 leads to a slippery argument about the empty function; the uninterested reader may start his induction at 1 instead of 0). Unquote.Induction from 1 is no problem.The slippery argument stuff (and other similar pearls thoughout the book) sends me wild.What is the slippery argument.Please.Anyone.With thanks to Paul Halmos for making my life 'miserably interesting' (sic)!!

Reviews (3)

Good but unclear
This book has a good converage of the material, but is often unclear from overmuch terseness.For example, I puzzled over the notation in one problem only to find it was explained in the caption to a figure!

Extremely helpful!
Kaplansky's Set Theory and Metric Spaces is one of the most helpful math books that I've ever used.Begining with basic set theory and covering such topics as cardinal numbers, countability, the Axiom of Choice, Zorn's Lemma, well ordering, basic properties of metric spaces, completeness, separability, and compactness, this book covered all of the main topics in my set theory class.Kaplansky's explanations are clear and concise, his examples are illuminating, and the problems are challenging without being far too difficult.As a bonus, this book is quite resonably priced.A must for anyone who is taking a first or second set theory class!

Reviews (2)

Kunen is the master expositor
This is the most widely used textbook for graduate -level set theory, andwith good reason. Kunen manages to cover all the essentials of set theoryin a quick 300 pages--and he does so with exceptional clarity and depth.

I purchased a copy of the book when it was first published in 1980; Iwas a graduate student at the time, studying set theory. The book was good,but perhaps a bit advanced for the independent study approach that I wastaking.

Some years later when I had the opportunity to teach agraduate-level course in set theory, using Kunen's text, I realized that asan adjunct to a lecture-based course, this book is ideal. I have also foundthat it clarifies subtle points about set theory that most authors glossover. For instance, his treatment makes very clear how to define theforcing relation in the ground model; why inaccessibles can't be provenconsistent with ZFC using ZFC alone; how transfinite recursion should beformally stated in the theory and how it is to be used formally; and whatthe different approaches to forcing are.

The main topics in the book areconstructibility (developed on the basis of an understanding of ordinaldefinability) and forcing, with a final chapter on iterated forcing. Loadsof material can be found in the vast number of exercises which, especiallyin the later chapters, provide a quick survey of important results in theliterature.

Kunen's style is both entertaining and precise. Everysentence has the extraordinary quality of literally bursting withinformation. One can easily go back to this book year after year and expectnew layers of insight to unfold. Kunen demonstrates both his mastery of settheory and mastery of the language in this superb text.