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Universal co-analytic sets


Author: Greg Hjorth
Journal: Proc. Amer. Math. Soc. 124 (1996), 3867-3873
MSC (1991): Primary 04A15
DOI: https://doi.org/10.1090/S0002-9939-96-03494-6
MathSciNet review: 1343698
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [Ba] Jon Barwise, Admissible sets and structures, Springer-Verlag, Berlin-New York, 1975. An approach to definability theory; Perspectives in Mathematical Logic. MR 0424560
  • [Je] Thomas Jech, Set theory, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. Pure and Applied Mathematics. MR 506523
  • [Ke] A. S. Kechris, Lectures on definable group actions and equivalence relations, Unpublished manuscript.
  • [Mi] Arnold W. Miller, Arnie Miller’s problem list, Set theory of the reals (Ramat Gan, 1991) Israel Math. Conf. Proc., vol. 6, Bar-Ilan Univ., Ramat Gan, 1993, pp. 645–654. MR 1234292
  • [Mo] Yiannis N. Moschovakis, Descriptive set theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland Publishing Co., Amsterdam-New York, 1980. MR 561709
  • [Sa] Gerald E. Sacks, Countable admissible ordinals and hyperdegrees, Advances in Math. 20 (1976), no. 2, 213–262. MR 0429523, https://doi.org/10.1016/0001-8708(76)90187-0

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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: https://doi.org/10.1090/S0002-9939-96-03494-6
Received by editor(s): May 2, 1994
Received by editor(s) in revised form: June 12, 1995
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1996 American Mathematical Society