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arXiv · 2007.04088

Metric groups, unitary representations and continuous logic

Aleksander Ivanov
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Abstract

We describe how properties of metric groups and of unitary representations of metric groups can be presented in continuous logic. In particular we find $L_{\omega_1 \omega}$-axiomatization of amenability. We also show that in the case of locally compact groups some uniform version of the negation of Kazhdan's property {\bf (T)} can be viewed as a union of first-order axiomatizable classes. We will see when these properties are preserved under taking elementary substructures.

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Aleksander Ivanov. 2020-07-06. Metric groups, unitary representations and continuous logic. https://doi.org/10.2478/cm-2021-0007

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