Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T10:58:01.905Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

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]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