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Metric groups, unitary representations and continuous logic
2021
Communications in Mathematics
We describe how properties of metric groups and of unitary representations of metric groups can be presented in continuous logic. In particular we find Lω 1 ω -axiomatization of amenability. We also show that in the case of locally compact groups some uniform version of the negation of Kazhdan's property (T) can be viewed as a union of first-order axiomatizable classes. We will see when these properties are preserved under taking elementary substructures.
doi:10.2478/cm-2021-0007
fatcat:l46fq7jqnra4jlwmblfxe3foma