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.

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 (4)

Excellent as a follow-up to Kunen
I'm a graduate student in set theory and I'm finding Kanamori an excellent follow-up to Kunen.The book manages to combine detailed technical exposition with historical insight which is actually useful to understanding the material (not just a list of dates) and gives one a "feel" for the subject.

Occasional excersises are contained which are good to help check if you're keeping up (though sometimes the hints are a little too complete: it might be better if these were relegated to an appendix).

The notation is a little non-standard, but not annoyingly so (f``X for f[X] is about as bad as it gets).

I believe this is pretty much the only book in which much of this material is collected together, so it's pretty much essential to any-one seriously interested in Set Theory.I await the promised second and third volumes with anticipation!

New edition available
A new edition of this book is available from Springer now, for a lower list price (and one third off if you have ever published in a Springer publication, like LNCS, LNM etc.).

Isbn: 0387517006
Sales Rank: 2316674

Isbn: 311015708X
Sales Rank: 1389626
Subjects:  1. Forcing (Model theory)    2. Logic    3. Mathematics    4. Model Theory    5. Science/Mathematics   

Isbn: 0821850911
Sales Rank: 525165
Subjects:  1. Science/Mathematics    2. Set theory    3. Topological Groups    4. Topology   

Reviews (1)

Isbn: 0387574948
Sales Rank: 2030575
Subjects:  1. Constructive mathematics    2. Foundations Of Mathematics    3. Science/Mathematics    4. Set Theory   

Isbn: 3540619380
Sales Rank: 3414119
Subjects:  1. Constructibility (Set theory)    2. Large cardinals (Mathematics)    3. Mathematics    4. Science/Mathematics    5. Set Theory   

Isbn: 0444701990
Sales Rank: 2891955
Subjects:  1. Science/Mathematics   

Isbn: 3110167778
Sales Rank: 1637669
Subjects:  1. Forcing (Model theory)    2. Mathematics    3. Science/Mathematics    4. Set Theory   

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Subjects:  1. Classification    2. Equivalence classes (Set theor    3. Equivalence classes (Set theory)    4. Equivalence relations (Set the    5. Equivalence relations (Set theory)    6. General    7. Mathematics    8. Science/Mathematics    9. Set Theory   

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Subjects:  1. Algebra, Boolean    2. General    3. Lifting theory    4. Mathematics    5. Science/Mathematics    6. Set Theory   

Isbn: 082181091X
Sales Rank: 2232590
Subjects:  1. Mathematics    2. Science/Mathematics    3. Set Theory   

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Sales Rank: 1299191
Subjects:  1. Constructibility (Set theory)    2. Large cardinals (Mathematics)    3. Logic    4. Mathematics    5. Medical    6. Set Theory   

Isbn: 0821811800
Sales Rank: 1920095
Subjects:  1. Forcing (Model theory)    2. Mathematics    3. Science/Mathematics    4. Set Theory   

Isbn: 0821834509
Sales Rank: 1977527
Subjects:  1. Borel sets    2. Continuum hypothesis    3. Descriptive set theory    4. Forcing (Model theory)    5. Mathematical Analysis    6. Mathematics    7. Science/Mathematics    8. Set Theory   

Isbn: 156881044X
Sales Rank: 1449780
Subjects:  1. Mathematics    2. Science/Mathematics    3. Set Theory   

Isbn: 0821836048
Sales Rank: 204820
Subjects:  1. Forcing (Model theory)    2. General    3. Logic    4. Mathematics    5. Science/Mathematics    6. Set theory