Aleksander Ivanov
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Metric groups, unitary representations and continuous logic
cm:9526 -
Communications in Mathematics,
April 30, 2021,
Volume 29 (2021), Issue 1 (Special Issue: Ostrava Mathematical Seminar)
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https://doi.org/10.2478/cm-2021-0007
Metric groups, unitary representations and continuous logic
Authors: Aleksander Ivanov
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Aleksander Ivanov
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.