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Nonstandard models and analytic equivalence relations

Author(s): Sy D. Friedman; Boban Velickovic
Journal: Proc. Amer. Math. Soc. 125 (1997), 1807-1809.
MSC (1991): Primary 04A15, 03C75
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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:

1.: L. Harrington and S. Shelah, Counting equivalence classes for co- $\kappa$ -Souslin equivalence relations, Logic Colloquium '80, North-Holland, 1982, pp. 147-152. MR 84c:03088
2.: G. Hjorth, Thin analytic equivalence relations and effective decompositions, J. Symbolic Logic. 58 (1993), 1153-1164. MR 95c:03119
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.: J. H. Silver, Counting the number of equivalence classes for Borel and coanalytic equivalence relations, Ann. Math. Logic 18 (1980), 1-28. MR 81d:03051


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