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Glimm-Effros for coanalytic equivalence relations

Published online by Cambridge University Press:  12 March 2014

Greg Hjorth
Greg Hjorth*
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, Parkville Victoria. 3010., Australia, E-mail: greg.hjorth@gmail.com
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Abstract

Assuming every real has a sharp, we prove that for any equivalence relation either Borel reduces E0 or in a manner allows the assignment of bounded subsets of ω1 as complete invariants.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 2 , June 2009 , pp. 402 - 422
Copyright
Copyright © Association for Symbolic Logic 2009

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References

REFERENCES

[1]Barwise, J., Admissible sets and structures, Springer-Verlag. 1975.CrossRefGoogle Scholar
[2]Ditzen, A., Ph.D. thesis, Caltech, 1992.Google Scholar
[3]Foreman, M. and Magidor, M., Large cardinals and definable counterexamples to the continuum hypothesis. Annals of Pure and Applied Logic, vol. 76 (1995). pp. 47–97.CrossRefGoogle Scholar
[4]Harrington, L., Kechris, A.S., and Louveau, A., A Glimm-Effros dichotomy for Borel equivalence relations, Journal of the American Mathematical Society, vol. 3 (1990), pp. 903–928.CrossRefGoogle Scholar
[5]Harrington, L. and Shelah, S., Counting equivalence classes for co-K-Souslin equivalence relations. Logic Colloquium '80 (Prague, 1980), Stud. Logic Foundations Math., vol. 108, North-Holland, 1982. pp. 147–152.Google Scholar
[6]Hjorth, G. and Kechris, A.S., Analytic equivalence relations and Vim-type classifications, this Journal, vol. 60 (1995), pp. 1273–1300.Google Scholar
[7]Hjorth, G. and Kechris, A.S., New dichotomies for Borel equivalence relations. The Bulletin of Symbolic Logic, vol. 3 (1997), pp. 329–346.CrossRefGoogle Scholar
[8]Jackson, S., A computation of . Memoirs of the American Mathematical Society, vol. 140 (1999).CrossRefGoogle Scholar
[9]Jech, T., Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich. Publishers], 1978.Google Scholar
[10]Kanovei, V., Linearization of definable order relations. Annals of Pure and Applied Logic, vol. 102 (2000), pp. 69–100.CrossRefGoogle Scholar
[11]Keisler, H.J., Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers, Studies in Logic and the Foundations of Mathematics, vol. 62, North-Holland Publishing Co., 1971.Google Scholar
[12]Moschovakis, Y.N., Descriptive set theory. Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland Publishing Co., 1980.Google Scholar