## Journal of Symbolic Logic

### A metamathematical condition equivalent to the existence of a complete left invariant metric for a Polish group

Alex Thompson

#### 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.

#### Article information

Source
J. Symbolic Logic, Volume 71, Issue 4 (2006), 1108-1124.

Dates
First available in Project Euclid: 20 November 2006

https://projecteuclid.org/euclid.jsl/1164060447

Digital Object Identifier
doi:10.2178/jsl/1164060447

Mathematical Reviews number (MathSciNet)
MR2275851

Zentralblatt MATH identifier
1105.03041

#### Citation

Thompson, Alex. A metamathematical condition equivalent to the existence of a complete left invariant metric for a Polish group. J. Symbolic Logic 71 (2006), no. 4, 1108--1124. doi:10.2178/jsl/1164060447. https://projecteuclid.org/euclid.jsl/1164060447

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