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| Softcover ISBN: | 978-0-8218-4453-3 |
| Product Code: | ULECT/44 |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $55.20 |
| eBook ISBN: | 978-1-4704-2188-5 |
| Product Code: | ULECT/44.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $52.00 |
| Softcover ISBN: | 978-0-8218-4453-3 |
| eBook ISBN: | 978-1-4704-2188-5 |
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| List Price: | $134.00 $101.50 |
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Book DetailsUniversity Lecture SeriesVolume: 44; 2008; 240 ppMSC: Primary 03
Over the last 20 years, the theory of Borel equivalence relations and related topics have been very active areas of research in set theory and have important interactions with other fields of mathematics, like ergodic theory and topological dynamics, group theory, combinatorics, functional analysis, and model theory. The book presents, for the first time in mathematical literature, all major aspects of this theory and its applications.
This book should be of interest to a wide spectrum of mathematicians working in set theory as well as the other areas mentioned. It provides a systematic exposition of results that so far have been only available in journals or are even unpublished. The book presents unified and in some cases significantly streamlined proofs of several difficult results, especially dichotomy theorems. It has rather minimal overlap with other books published in this subject.
ReadershipGraduate students and research mathematicians interested in logic, set theory, and applications.
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Table of Contents
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Chapters
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Introduction
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Chapter 1. Descriptive set theoretic background
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Chapter 2. Some theorems of descriptive set theory
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Chapter 3. Borel ideals
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Chapter 4. Introduction to equivalence relations
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Chapter 5. Borel reducibility of equivalence relations
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Chapter 6. “Elementary” results
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Chapter 7. Introduction to countable equivalence relations
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Chapter 8. Hyperfinite equivalence relations
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Chapter 9. More on countable equivalence relations
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Chapter 10. The 1st and 2nd dichotomy theorems
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Chapter 11. Ideal $\mathcal {I}_1$ and the equivalence relation $\mathsf {E}_1$
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Chapter 12. Actions of the infinite symmetric group
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Chapter 13. Turbulent group actions
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Chapter 14. The ideal $\mathcal {I}_3$ and the equivalence relation $\mathsf {E}_3$
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Chapter 15. Summable equivalence relations
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Chapter 16. $\mathsf {c}_0$-equalities
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Chapter 17. Pinned equivalence relations
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Chapter 18. Reduction of Borel equivalence relations to Borel ideals
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Appendix A. On Cohen and Gandy–Harrington forcing over countable models
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Additional Material
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Reviews
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The book is rather self-contained, starting with a quick but detailed presentation of basic results from descriptive set theory needed in the sequel, and ending with a brief addendum on forcing, and more particularly on Gandy–Harrington forcing, which is extensively used in the proofs.
Mathematical Reviews
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
Over the last 20 years, the theory of Borel equivalence relations and related topics have been very active areas of research in set theory and have important interactions with other fields of mathematics, like ergodic theory and topological dynamics, group theory, combinatorics, functional analysis, and model theory. The book presents, for the first time in mathematical literature, all major aspects of this theory and its applications.
This book should be of interest to a wide spectrum of mathematicians working in set theory as well as the other areas mentioned. It provides a systematic exposition of results that so far have been only available in journals or are even unpublished. The book presents unified and in some cases significantly streamlined proofs of several difficult results, especially dichotomy theorems. It has rather minimal overlap with other books published in this subject.
Graduate students and research mathematicians interested in logic, set theory, and applications.
-
Chapters
-
Introduction
-
Chapter 1. Descriptive set theoretic background
-
Chapter 2. Some theorems of descriptive set theory
-
Chapter 3. Borel ideals
-
Chapter 4. Introduction to equivalence relations
-
Chapter 5. Borel reducibility of equivalence relations
-
Chapter 6. “Elementary” results
-
Chapter 7. Introduction to countable equivalence relations
-
Chapter 8. Hyperfinite equivalence relations
-
Chapter 9. More on countable equivalence relations
-
Chapter 10. The 1st and 2nd dichotomy theorems
-
Chapter 11. Ideal $\mathcal {I}_1$ and the equivalence relation $\mathsf {E}_1$
-
Chapter 12. Actions of the infinite symmetric group
-
Chapter 13. Turbulent group actions
-
Chapter 14. The ideal $\mathcal {I}_3$ and the equivalence relation $\mathsf {E}_3$
-
Chapter 15. Summable equivalence relations
-
Chapter 16. $\mathsf {c}_0$-equalities
-
Chapter 17. Pinned equivalence relations
-
Chapter 18. Reduction of Borel equivalence relations to Borel ideals
-
Appendix A. On Cohen and Gandy–Harrington forcing over countable models
-
The book is rather self-contained, starting with a quick but detailed presentation of basic results from descriptive set theory needed in the sequel, and ending with a brief addendum on forcing, and more particularly on Gandy–Harrington forcing, which is extensively used in the proofs.
Mathematical Reviews
