Aleksander Ivanov
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Metric groups, unitary representations and continuous logic
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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
0000-0002-5720-2864
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.
Ivanov, Aleksander, 2021, Unbounded Actions Of Metric Groups And Continuous Logic, Zeitschrift FĂźr Mathematische Logik Und Grundlagen Der Mathematik, 67, 2, pp. 206-225, 10.1002/malq.202000050.