Vaught's conjecture on analytic sets

Author:
Greg Hjorth

Journal:
J. Amer. Math. Soc. **14** (2001), 125-143

MSC (2000):
Primary 03E15

DOI:
https://doi.org/10.1090/S0894-0347-00-00349-0

Published electronically:
September 18, 2000

MathSciNet review:
1800351

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Let be a Polish group. We characterize when there is a Polish space with a continuous -action and an analytic set (that is, the Borel image of some Borel set in some Polish space) having uncountably many orbits but no perfect set of orbit inequivalent points.

Such a Polish -space and analytic exist exactly when there is a continuous, surjective homomorphism from a closed subgroup of onto the infinite symmetric group, , consisting of all permutations of equipped with the topology of pointwise convergence.

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Additional Information

**Greg Hjorth**

Affiliation:
Department of Mathematics, University of California, Los Angeles, California 90095-1555

Email:
greg@math.ucla.edu

DOI:
https://doi.org/10.1090/S0894-0347-00-00349-0

Keywords:
Polish group,
group actions,
topological Vaught conjecture

Received by editor(s):
June 8, 1998

Received by editor(s) in revised form:
June 22, 2000

Published electronically:
September 18, 2000

Additional Notes:
The author’s research was partially supported by NSF grant DMS 96-22977.

Article copyright:
© Copyright 2000
American Mathematical Society