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On polish groups admitting a compatible complete left-invariant metric
Journal of Symbolic Logic 76 (2):437 - 447 (2011)
Abstract
We prove that the set of all Polish groups admitting a compatible complete left-invariant metric (called CLI) is coanalytic non-Borel as a subset of a standard Borel space of all Polish groups. As an application of this result, we show that there does not exist a weakly universal CLI group. This, in particular, answers in the negative a question of H.BeckerOther Versions
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Citations of this work
A Hierarchy on Non-Archimedean Polish Groups Admitting a Compatible Complete Left-Invariant Metric.Longyun Ding & Xu Wang - 2026 - Journal of Symbolic Logic 91 (2):680-698.
Polish G-spaces and continuous logic.A. Ivanov & B. Majcher-Iwanow - 2017 - Annals of Pure and Applied Logic 168 (4):749-775.
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