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Borel Equivalence Relations: Structure and Classification

About this Title

Vladimir Kanovei, Institute for Information Transmission Problems, Moscow, Russia

Publication: University Lecture Series
Publication Year: 2008; Volume 44
ISBNs: 978-0-8218-4453-3 (print); 978-1-4704-2188-5 (online)
DOI: https://doi.org/10.1090/ulect/044
MathSciNet review: MR2441635
MSC: Primary 03E15; Secondary 28D99, 37A20

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Table of Contents

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Front/Back Matter

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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