Set Theory An Introduction To Independence Proofs (Studies in Logic and the Foundations of Mathematics) [Paperback]

Kenneth Kunen (Author)

Book Description

ISBN-10: 0444868399 | ISBN-13: 978-0444868398 | Publication Date: December 15, 1983

Many branches of abstract mathematics have been affected by the modern independence proofs in set theory. This book provides an introduction to relative consistency proofs in axiomatic set theory, and is intended to be used as a text in beginning graduate courses in that subject. It is hoped that this treatment will make the subject accessible to those mathematicians whose research is sensitive to axiomatics. The readers should have had the equivalent of an undergraduate course on cardinals and ordinals, but no specific training in logic is necessary. The volume includes a discussion of modern techniques in forcing, as well as coverage of infinitary combinatorics and its relevance to independence proofs. The work also features a lucid treatment of basic facts about constructibility.

Editorial Reviews

Review

...provides a good introduction to relative consistence proofs in axiomatic set theory. It can be recommended as a graduate text on the subject. -- Zentralblatt für Mathematik

Product Details

• Paperback: 330 pages
• Publisher: North Holland (December 15, 1983)
• Language: English
• ISBN-10: 0444868399
• ISBN-13: 978-0444868398
• Product Dimensions: 8.4 x 5.4 x 0.9 inches
• Shipping Weight: 15.5 ounces (View shipping rates and policies)
• Average Customer Review: 4.4 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #1,005,812 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

32 of 33 people found the following review helpful:

5.0 out of 5 stars Kunen is the master expositor, August 23, 1998

By 

Paul Corazza (Fairfield, IA) - See all my reviews

This review is from: Set Theory An Introduction To Independence Proofs (Studies in Logic and the Foundations of Mathematics) (Paperback)

This is the most widely used textbook for graduate -level set theory, and with good reason. Kunen manages to cover all the essentials of set theory in 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; I was 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 was taking.

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

The main topics in the book are constructibility (developed on the basis of an understanding of ordinal definability) and forcing, with a final chapter on iterated forcing. Loads of material can be found in the vast number of exercises which, especially in the later chapters, provide a quick survey of important results in the literature.

Kunen's style is both entertaining and precise. Every sentence has the extraordinary quality of literally bursting with information. One can easily go back to this book year after year and expect new layers of insight to unfold. Kunen demonstrates both his mastery of set theory and mastery of the language in this superb text.

15 of 15 people found the following review helpful:

3.0 out of 5 stars For better or worse it's the standard, July 11, 2005

By 

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

This review is from: Set Theory An Introduction To Independence Proofs (Studies in Logic and the Foundations of Mathematics) (Paperback)

For a graduate course on set theory, I don't think there is any serious competition for Kunen. It assumes you have already had a basic course and starts right in using the concepts of axiomatic set theory and the properties of cardinals and ordinals, although it does start with a terse recap of logic and ZFC. The whole book is narrowly focused on leading up to the technique of forcing to prove consistency results under ZFC. It mostly avoids large cardinals, the Axiom of Choice, descriptive set theory, and model theory.

The style is fairly readable, but I thought it was a little too messy for clarity. Without the key points being highlighted, I tended to get lost in the details. The early chapters have few exercises and not many examples. The last chapter on forcing is the big payoff of the book and has lots of exercises, but still a shortage of examples.

I don't think it makes a good reference, because it is not concise and clear enough. The monograph by Jech (3rd edition!) is vastly better for that. Even if you are currently using Kunen for a class, it is worth referring to Jech to clarify points in Kunen.

11 of 14 people found the following review helpful:

5.0 out of 5 stars Excellent graduate level text, May 17, 1997

By A Customer

This review is from: Provability, Computability and Reflection, Volume 102 (Studies in Logic and the Foundations of Mathematics) (Paperback)

An excellent text leading to a clear explanation of forcing and what it is good for. Tough going without someone to question for this advanced non-student (almost a math minor but 20 years ago.) This was recommended in sci.math as the best approach to forcing and I believe it