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A Metamathematical Condition Equivalent to the Existence of a Complete Left Invariant Metric for a Polish Group

Published online by Cambridge University Press:  12 March 2014

Alex Thompson*
Affiliation:
Mathematics Department, UCLA, Los Angeles, CA 90095-1555, USA, E-mail: act2@math.ucla.edu, URL: www.math.ucla.edu/~act2

Abstract

Strengthening a theorem of Hjorth this paper gives a new characterization of which Polish groups admit compatible complete left invariant metrics. As a corollary it is proved that any Polish group without a complete left invariant metric has a continuous action on a Polish space whose associated orbit equivalence relation is not essentially countable.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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A Metamathematical Condition Equivalent to the Existence of a Complete Left Invariant Metric for a Polish Group
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