The Structure of Borel Equivalence Relations in Polish Spaces
An exposition of recent work on Borel equivalence relations in Polish spaces is presented. This includes a general Glimm-Effros dichotomy for Borel equivalence relations and a study of countable Borel equivalence relations and their classification into subclasses such as smooth, hyperfinite, amenable, treeable etc.
KeywordsEquivalence Relation Polish Space Continuum Hypothesis Countable Group Jordan Canonical Form
Unable to display preview. Download preview PDF.
- 6.R. Dellacherie and P-A. Meyer, Therie discrete du potentiel, Hermann, 1983.Google Scholar
- 7.R. Dougherty, S. Jackson and A. Kechris, The structure of equivalence relations on Polish spaces, I; An extension of the Glimm-Effros dichotomy, circulated notes, March 1989.Google Scholar
- 8.R. Dougherty, S. Jackson and A. Kechris, The structure of equivalence relations on Polish spaces, II; Countable equivalence relations or descriptive dynamics, circulated notes, March 1989.Google Scholar
- 10.E. Effiros, Polish transformation groups and classification problems, General Topology and Modern Analysis, Rao and McAuley, eds. (1980), Academic Press, 217–227.Google Scholar
- 19.K. Kada, A Borel version of Dilworth’s theorem, (to appear).Google Scholar
- 21.A. Kechris, Amenable equivalence relations and Turing degrees, J. Symb. Logic (to appear).Google Scholar
- 29.T. Slaman and J. Steel, Definable functions on degrees, in “Cabal Seminar 81–85”, Lecture Notes in Math. 1333, Springer-Verlag, 1988, 37–55.Google Scholar
- 30.J. Steel, Long games, in “Cabal Seminar 81–85”, Lecture notes in Math. 1333, Springer-Verlag, 1988, 56–97.Google Scholar