Set Theory

Rating:
Summary: Excellent graduate level text
Review: 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

Rating:
Summary: Kunen is the master expositor
Review: 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.

Rating:
Summary: Kunen is the master expositor
Review: 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.