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 | References | Similar Articles | Additional Information

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