Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)



The classification of hypersmooth
Borel equivalence relations

Authors: Alexander S. Kechris and Alain Louveau
Journal: J. Amer. Math. Soc. 10 (1997), 215-242
MSC (1991): Primary 04A15, 03E15
MathSciNet review: 1396895
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [DJK] R. Dougherty, S. Jackson and A. S. Kechris, The structure of hyperfinite Borel equivalence relations, Trans. Amer. Math. Soc., 341 (1), 193-225, 1994. MR 94c:03066
  • [FR] J. Feldman and A. Ramsey, Countable sections for free actions of groups, Adv. Math., 55, 224-227, 1985. MR 86h:28011
  • [FS] H. Friedman and L. Stanley, A Borel reducibility theory for classes of countable structures, J. Symb. Logic, 54 (3), 894-914, 1989. MR 91f:03062
  • [HKL] L. Harrington, A. S. Kechris and A. Louveau, A Glimm-Effros dichotomy for Borel equivalence relations, J. Amer. Math. Soc., 3 (4), 903-927, 1990. MR 91h:28023
  • [HMS] L. Harrington, D. Marker and S. Shelah, Borel orderings, Trans. Amer. Math. Soc., 310, 292-302, 1988. MR 90c:03041
  • [JKL] S. Jackson, A. S. Kechris and A. Louveau, On countable Borel equivalence relations, to appear.
  • [K1] A. S. Kechris, Countable sections for locally compact group actions, Ergod. Th. & Dynam. Sys., 12, 283-295, 1992. MR 94b:22003
  • [K2] -, Countable sections for locally compact group actions, II, Proc. Amer. Math. Soc., 120, 241-247, 1994. MR 94b:22004
  • [K3] -, Classical Descriptive Set Theory, Springer-Verlag, New York, 1995. MR 96e:03057
  • [L] A. Louveau, On the reducibility order between Borel equivalence relations, Stud. Logic Found. Math., vol. 134, North-Holland, Amsterdam, 1994. MR 96g:03081
  • [Mi] D. Miller, On the measurability of orbits in Borel actions, Proc. Amer. Math. Soc., 63, 165-170, 1977. MR 55:13394
  • [Mo] Y. N. Moschovakis, Descriptive Set Theory, North Holland, Amsterdam, 1980. MR 82e:03002
  • [R] J. T. Rogers, Jr., Borel transversals and ergodic measures on indecomposable continua, Topology and its Appl., 24, 217-227, 1986. MR 88a:54078
  • [S] J. H. Silver, Counting the number of equivalence classes of Borel and coanalytic equivalence relations, Ann. Math. Logic. 18, 1-28, 1980. MR 81d:03051
  • [V] A. M. Vershik, Trajectory Theory, in Ya. G. Sinai (Ed.), Dynamical Systems II, Springer-Verlag, 77-98, 1989. MR 91i:58079
  • [VF] A. M. Vershik and A. L. Fedorov, Trajectory Theory, J. Soviet Math., 38 (2), 1799-1822, 1987. MR 88b:28031
  • [VG] V. G. Vinokurov and N. N. Ganikhodzhaev, Conditional functions in the trajectory theory of dynamical systems, Math. USSR Izvestija, 13 (2), 221-252, 1979. MR 80d:28038
  • [W] V. M. Wagh, A descriptive version of Ambrose's representation theorem for flows, Proc. Ind. Acad. Sci. (Math. Sci.), 98, 101-108, 1988. MR 90m:28021

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 04A15, 03E15

Retrieve articles in all journals with MSC (1991): 04A15, 03E15

Additional Information

Alexander S. Kechris
Affiliation: Department of Mathematics, A. P. Sloan Laboratory of Mathematics and Statistics, California Institute of Technology, Pasadena, California 91125

Alain Louveau
Affiliation: Equipe d’Analyse, Université Paris VI, 4, Place Jussieu, 75230 Paris Cedex 05, France

Keywords: Borel equivalence relations, hypersmooth, dichotomy theorems
Received by editor(s): September 1, 1994
Received by editor(s) in revised form: June 11, 1996
Additional Notes: The first author’s research was partially supported by NSF Grant DMS-9317509
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society