Theory of Countable Borel Equivalence Relations

"This book surveys the state of the art in a very active research area in descriptive set theory, which has important connections to many areas of mathematics, including group theory, dynamical systems, and operator algebras. It will be of great value to beginning graduate students and researchers in these areas"--

List of contents

1. Equivalence relations and reductions; 2. Countable Borel equivalence relations; 3. Essentially countable relations; 4. Invariant and quasi-invariant measures; 5. Smoothness, $\mathbf{E}_0$ and $\mathbf{E}_\infty$; 6. Rigidity and incomparability; 7. Hyperfiniteness; 8. Amenability; 9. Treeability; 10. Freeness; 11. Universality; 12. The poset of bireducibility types; 13. Structurability; 14. Topological realizations; 15. A universal space for actions and equivalence relations; 16. Open problems; References; List of Notation; Subject Index.

About the author

Alexander S. Kechris is Professor of Mathematics at the California Institute of Technology. He is the recipient of numerous honors, including the Sloan Research Fellowship, the J. S. Guggenheim Memorial Foundation Fellowship, and the Carol Karp Prize of the Association for Symbolic Logic. He is also an Inaugural Fellow of the American Mathematical Society.

Product details

• Authors: Alexander S Kechris, Alexander S. Kechris, Alexander S. (California Institute of Tec Kechris
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 01.11.2024
• EAN: 9781009562294
• ISBN: 978-1-0-0956229-4
• No. of pages: 174
• Series: Cambridge Tracts in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Basic principles; MATHEMATICS / Group Theory, MATHEMATICS / Functional Analysis, MATHEMATICS / Set Theory, Groups & group theory, Functional analysis & transforms, Groups and group theory, Functional analysis and transforms, Set theory