Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-28T16:25:16.633Z Has data issue: false hasContentIssue false

A dichotomy for the definable universe

Published online by Cambridge University Press:  12 March 2014

Greg Hjorth*
Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, California 91125, E-mail: greg@cco.caltech.edu

Abstract

In the presence of large cardinals, or sufficient determinacy, every equivalence relation in either admits a wellordered separating family or continuously reduces E0.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Christensen, J. P. R., Topology and Borel structure, North-Holland, Amsterdam, 1974.Google Scholar
[2]Ditzen, A., Definable equivalence relations on Polish spaces, Ph.D. Thesis, California Institute of Technology, Pasadena, California, 1992.Google Scholar
[3]Harrington, L. A., Kechris, A. S., and Louveau, A., A Glimm-Effros dichotomy for Borel equivalence relations, Journal of the American Mathematical Society, vol. 3 (1990), pp. 903928.CrossRefGoogle Scholar
[4]Jech, T. J., Set theory, Academic Press, San Francisco, California, 1978.Google Scholar
[5]Kechris, A. S., Lectures on classical descriptive set theory (to appear).Google Scholar
[6]Moschovakis, Y. N., Descriptive set theory, North-Holland, Amsterdam, 1980.Google Scholar
[7]Shelah, S. and Woodin, H., Large cardinals imply that every reasonably definable set of reals is Lebesque measurable, Israel Journal of Mathematics, vol. 70 (1990), pp. 381393.CrossRefGoogle Scholar
[8]Silver, J. H., Counting the number of equivalence classes of Borel and coanalytic equivalence relations, Annals of Mathematical Logic, vol. 18 (1980), pp. 128.CrossRefGoogle Scholar