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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

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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