Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.
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Editorial Reviews
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Overall, the general impression is very good and this book will become a standard reference for the field. The book contains material from many perspective concerning descriptive set theory. I highly recommend it to any reader. -- R. Daniel Mauldin, Journal of Symbolic Logic, December 1997
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Most Helpful Customer Reviews
13 of 13 people found the following review helpful:
3.0 out of 5 stars
Not much alternative to this,
By Nathan Oakes (Ashland, Oregon) - See all my reviews
This review is from: Classical Descriptive Set Theory (Graduate Texts in Mathematics) (v. 156) (Hardcover)
There is a bit of unintended humor in the preface: "This book is essentially self-contained. The only thing it requires is familiarity...with the basics of general topology, measure theory, and functional analysis, as well as the elements of set theory..."
He says the target is the beginning graduate. I would place it better as a 2nd-year grad course. The text is dense and moves fast. Readability is pretty low. He never introduces a topic with context or overview. Extensive references to the literature were deliberately left out, which I think is wrong since it is a textbook. On the plus side, it is sprinkled with many exercises. (BTW, this is one of those cases that make you wish Springer didn't make authors do their own typesetting.) There are only three common texts for descriptive set theory: Kechris, Jech, and Moschovakis. Jech has less detail on Polish spaces, Borel sets, and co-analytic sets, so it is not really a substitute, but its conciseness is nice and it makes a good companion. Moschovakis was a big deal when it came out because it collected a lot of information for the first time. But I don't think it is so good in content or style that you should be concerned if you have only Kechris and Jech.
9 of 10 people found the following review helpful:
5.0 out of 5 stars
Excellent reference,
By A.T. (Los Angeles) - See all my reviews
This review is from: Classical Descriptive Set Theory (Graduate Texts in Mathematics) (v. 156) (Hardcover)
A truly outstanding reference for the purely classical aspects of descriptive set theory, it falls under Kelley's label, "What every young set theorist needs to know." It is not an easy book for the beginner as it is very concise and gives little motivation, but for the advanced student it is essential.
As a Ph.D. student in the field, hardly a day goes by where I don't look up something in this book. I'm buying a new copy since my old one is falling apart.
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Inside This Book
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First Sentence:
A topological space is a pair (X, T), where X is a set and T a collection of subsets of X such that , X T and T is closed under arbitrary unions and finite intersections. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
generalized separation property, graph theoretic tree, uniformization property, projective determinacy, projective sets, projective hierarchy, finite splitting, perfect kernel, density topology, descriptive set theory, reflection theorem, meager sets, clopen sets, compact metrizable space, analytic sets, leftmost branch, transfinite sequence, periodicity theorems, basic open sets, open basis, nonempty open sets, continuous surjection, metrizable spaces, dense open sets, relative topology Key Phrases - Capitalized Phrases (CAPs): (learn more)
Projective Determinacy, Axiom of Choice, Saint Raymond, Baire Category, Effros Borel, Definable Determinacy, Lusin Separation Theorem, Novikov Separation Theorem, Basic Facts, The Periodicity Theorems, Souslin's Theorem, Borel Ei-complete, Hurewicz's Theorem, König's Lemma, Third Periodicity Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
A topological space is a pair (X, T), where X is a set and T a collection of subsets of X such that , X T and T is closed under arbitrary unions and finite intersections. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
generalized separation property, graph theoretic tree, uniformization property, projective determinacy, projective sets, projective hierarchy, finite splitting, perfect kernel, density topology, descriptive set theory, reflection theorem, meager sets, clopen sets, compact metrizable space, analytic sets, leftmost branch, transfinite sequence, periodicity theorems, basic open sets, open basis, nonempty open sets, continuous surjection, metrizable spaces, dense open sets, relative topology Key Phrases - Capitalized Phrases (CAPs): (learn more)
Projective Determinacy, Axiom of Choice, Saint Raymond, Baire Category, Effros Borel, Definable Determinacy, Lusin Separation Theorem, Novikov Separation Theorem, Basic Facts, The Periodicity Theorems, Souslin's Theorem, Borel Ei-complete, Hurewicz's Theorem, König's Lemma, Third Periodicity Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 13
books:
See all 13 books this book cites
100
books
cite this book:
See all 100 books citing this book
- Abstract Harmonic Analysis: Volume 2: Structure and Analysis for Compact Groups. Analysis on Locally Compact Abelian Groups (Grundlehren der mathematischen Wissenschaften) (v. 2) by Edwin Hewitt in Back Matter
- Theory of Correspondences: Including Applications to Mathematical Economics (Canadian Mathematical Society Series of Monographs & Advanced Texts) by Erwin Klein in Back Matter
- Notes on Set Theory (Undergraduate Texts in Mathematics) by Yiannis Moschovakis in Back Matter
- Measure Theory (Graduate Texts in Mathematics) (v. 18) by Paul R. Halmos in Back Matter
- Elements of Set Theory by Herbert B. Enderton in Back Matter
See all 13 books this book cites
- Descriptive Set Theory and Dynamical Systems (London Mathematical Society Lecture Note Series) by M. Foreman on page 257, page 270, and page 291
- Sets and Proofs (London Mathematical Society Lecture Note Series) by S. Barry Cooper on page 195, and page 364
- Algebra and Coalgebra in Computer Science: First International Conference, CALCO 2005, Swansea, UK, September 3-6, 2005, Proceedings (Lecture Notes in ... Computer Science and General Issues) by José Luis Fiadeiro on page 407
- 1,001 Low-Fat Vegetarian Recipes: Delicious, Easy-to-Make, Healthy Meals for Everyone by Sue Spitler on page 197
- Algebraic Geometry (Graduate Texts in Mathematics) by Robin Hartshorne in Front Matter
See all 100 books citing this book
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