Journal of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6834(e) ISSN 0894-0347(p)

A Glimm-Effros dichotomy for Borel equivalence relations

Author(s): L. A. Harrington; A. S. Kechris; A. Louveau
Journal: J. Amer. Math. Soc. 3 (1990), 903-928.
MSC: Primary 28E15; Secondary 03E15, 22D40
MathSciNet review: 1057041
Retrieve article in: PDF
This article is available free of charge

References:

[B1]: J. P. Burgess, Equivalences generated by families of Borel sets, Proc. Amer. Math. Soc. 69 (1978), 323-326. MR 0476524 (57:16084)
[B2]: -, A selection theorem for group actions, Pacific J. Math. 80 (1979), 333-336. MR 539418 (81a:54041)
[D]: J. Dixmier, ${C^ * }$ -algebras, North-Holland, 1977. MR 0458185 (56:16388)
[DJK1]: 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, 1989.
[DJK2]: -, The structure of equivalence relations on Polish spaces, II: Countable equivalence relations or descriptive dynamics, circulated notes, 1989.
[E1]: E. G. Effros, Transformation groups and ${C^ *}$ -algebras, Ann. of Math. 81 (1965), 38-55. MR 0174987 (30:5175)
[E2]: -, Polish transformation groups and classification problems, General Topology and Modern Analysis (Rao and Mc Auley, eds.), Academic Press, 1980, pp. 217-227. MR 619045 (82k:54064)
[Gl1]: J. Glimm, Type I ${C^ * }$ -algebras, Ann. of Math. 73 (1961), 572-612. MR 0124756 (23:A2066)
[Gl2]: -, Locally compact transformation groups, Trans. Amer. Math. Soc. 101 (1961), 124-138. MR 0136681 (25:146)
[Go]: G. Godefroy, Some remarks on Suslin sections, Fund. Math. 84 (1986), 159-167. MR 871854 (88h:54053)
[HMS]: L. Harrington, D. Marker, and S. Shelah, Borel orderings, Trans. Amer. Math. Soc. 310 (1988), 293-302. MR 965754 (90c:03041)
[Ka]: K. Kada, A Borel version of Dilworth's theorem (to appear).
[KW]: Y. Katznelson and B. Weiss, The construction of quasi-invariant measures, Israel J. Math. 12 (1972), 1-4. MR 0316679 (47:5226)
[Ke]: A. S. Kechris, Amenable equivalence relations and Turing degrees, J. Symbolic Logic (to appear). MR 1131739 (93c:03061)
[Kr1]: W. Krieger, On quasi-invariant measures on uniquely ergodic systems, Invent. Math. 14 (1971), 184-196. MR 0293060 (45:2139)
[Kr2]: -, On Borel automorphisms and their quasi-invariant measures, Math. Z. 151 (1976), 19-24. MR 0417389 (54:5439)
[Ku]: K. Kuratowski, Topology, vol. I, Academic Press, 1966. MR 0217751 (36:840)
[L]: A. Louveau, Two results on Borel orders, J. Symbolic Logic 34 (1989), 865-874. MR 1011175 (90i:03052)
[LS]: A. Louveau and J. Saint Raymond, On the quasi-ordering of Borel linear orders under embeddability, J. Symbolic Logic 55 (1990), 537-560. MR 1056369 (91h:03067)
[MK]: D. A. Martin and A. S. Kechris, Infinite games and effective descriptive set theory, Analytic Sets (C. A. Rogers et al., eds.), Academic Press, 1980. MR 562614 (81i:04003)
[M]: Y. Moschovakis, Descriptive set theory, North-Holland, 1980. MR 561709 (82e:03002)
[SW]: S. Shelah and B. Weiss, Measurable recurrence and quasi-invariant measures, Israel J. Math. 43 (1982), 154-160. MR 689974 (84d:28025)
[S]: J. H. Silver, Counting the number of equivalence classes of Borel and coanalytic equivalence relations, Ann. Math. Logic 18 (1980), 1-28. MR 568914 (81d:03051)
[U]: C. Uzcategui, Ph.D. Thesis, California Institute of Technology, 1990.
[W]: B. Weiss, Measurable dynamics, Contemporary Math. 26 (1984), 395-421. MR 737417 (85j:28027)
[Z]: R. J. Zimmer, Ergodic theory and semisimple groups, Birkhäuser, 1984. MR 776417 (86j:22014)

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|