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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Nonstandard models and analytic equivalence relations
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by Sy D. Friedman and Boban Velickovic PDF
Proc. Amer. Math. Soc. 125 (1997), 1807-1809 Request permission

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
  • Leo Harrington and Saharon Shelah, Counting equivalence classes for co-$\kappa$-Souslin equivalence relations, Logic Colloquium ’80 (Prague, 1980) Studies in Logic and the Foundations of Mathematics, vol. 108, North-Holland, Amsterdam-New York, 1982, pp. 147–152. MR 673790
  • Greg Hjorth, Thin equivalence relations and effective decompositions, J. Symbolic Logic 58 (1993), no. 4, 1153–1164. MR 1253912, DOI 10.2307/2275133
  • G. Hjorth and A. S. Kechris, Analytic equivalence relations and Ulm-type classifications, J. Symbolic Logic 60 (1995), 1273–1300.
  • 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, DOI 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
  • MR Author ID: 191285
  • Email: sdf@math.mit.edu
  • Boban Velickovic
  • Affiliation: Equipe de Logique, University of Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France
  • Email: boban@logique.jussieu.fr
  • 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
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 1807-1809
  • MSC (1991): Primary 04A15, 03C75
  • DOI: https://doi.org/10.1090/S0002-9939-97-03700-3
  • MathSciNet review: 1363419