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Universal co-analytic sets

Author(s): Greg Hjorth
Journal: Proc. Amer. Math. Soc. 124 (1996), 3867-3873.
MSC (1991): Primary 04A15
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Abstract: There is a universal $\Pi _{1}^{1}$ equivalence relation. The existence of a $\Pi _{1}^{1}$ set universal for $\Pi \hskip -3.5pt\lower 7.5pt\hbox {$\widetilde {}$}\hskip 2.3pt _{1}^{1}$ non-Borel is independent of the usual axioms of mathematics.

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T. Jech, Set theory, Academic Press, San Diego, 1978. MR 80a:03062

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A. S. Kechris, Lectures on definable group actions and equivalence relations, Unpublished manuscript.

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A. W. Miller, Arnie Miller's problem list, Set theory of the reals (H. Judah, ed.), IMCP, Bar-Ilan, 1993. MR 94m:03073

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Y. N. Moschovakis, Descriptive set theory, North-Holland Publishing Company, Amsterdam, New York, Oxford, 1980. MR 82e:03002

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G. E. Sacks, Countable admissible ordinals and hyperdegrees, Advances in Mathematics 19 (1976), 213-262. MR 55:2536

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Additional Information:

Greg Hjorth
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Address at time of publication: Department of Mathematics, University of California, Los Angeles, California 90024-1555
Email: greg@cco.caltech.edu, greg@math.ucla.edu

DOI: 10.1090/S0002-9939-96-03494-6
PII: S 0002-9939(96)03494-6
Received by editor(s): May 2, 1994
Received by editor(s) in revised form: June 12, 1995
Communicated by: Andreas R. Blass
Copyright of article: Copyright 1996, American Mathematical Society

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