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Vaught's conjecture and the Glimm-Effros property for Polish transformation groups


Authors: Greg Hjorth and Slawomir Solecki
Journal: Trans. Amer. Math. Soc. 351 (1999), 2623-2641
MSC (1991): Primary 04A15
DOI: https://doi.org/10.1090/S0002-9947-99-02141-8
Published electronically: March 10, 1999
MathSciNet review: 1467467
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Abstract: We extend the original Glimm-Effros theorem for locally compact groups to a class of Polish groups including the nilpotent ones and those with an invariant metric. For this class we thereby obtain the topological Vaught conjecture.


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Additional Information

Greg Hjorth
Affiliation: Department of Mathematics, 253–37, California Institute of Technology, Pasadena, California 91125
Address at time of publication: Department of Mathematics, MSB 6363, University of California, Los Angeles, California 90095-1555
Email: greg@math.ucla.edu

Slawomir Solecki
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: ssolecki@indiana.edu

DOI: https://doi.org/10.1090/S0002-9947-99-02141-8
Keywords: Polish group, orbit equivalence relation
Received by editor(s): August 18, 1995
Received by editor(s) in revised form: June 16, 1997
Published electronically: March 10, 1999
Article copyright: © Copyright 1999 American Mathematical Society

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