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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Nonstandard models
and analytic equivalence relations

Authors: Sy D. Friedman and Boban Velickovic
Journal: Proc. Amer. Math. Soc. 125 (1997), 1807-1809
MSC (1991): Primary 04A15, 03C75
MathSciNet review: 1363419
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Abstract: We improve a result of Hjorth concerning the nature of thin analytic equivalence relations. The key lemma uses a weakly compact cardinal to construct certain nonstandard models, which Hjorth obtained using $\#$'s.

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

  • 1. Leo Harrington and Saharon Shelah, Counting equivalence classes for co-𝜅-Souslin equivalence relations, Logic Colloquium ’80 (Prague, 1980) Stud. Logic Foundations Math., vol. 108, North-Holland, Amsterdam-New York, 1982, pp. 147–152. MR 673790
  • 2. Greg Hjorth, Thin equivalence relations and effective decompositions, J. Symbolic Logic 58 (1993), no. 4, 1153–1164. MR 1253912, 10.2307/2275133
  • 3. G. Hjorth and A. S. Kechris, Analytic equivalence relations and Ulm-type classifications, J. Symbolic Logic 60 (1995), 1273-1300. CMP 96:06
  • 4. Jack H. Silver, Counting the number of equivalence classes of Borel and coanalytic equivalence relations, Ann. Math. Logic 18 (1980), no. 1, 1–28. MR 568914, 10.1016/0003-4843(80)90002-9

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Additional Information

Sy D. Friedman
Affiliation: Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139

Boban Velickovic
Affiliation: Equipe de Logique, University of Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France

Received by editor(s): September 25, 1995
Received by editor(s) in revised form: November 20, 1995
Additional Notes: Research supported by NSF Contract # 92–05530.
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society