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Keywords:
Continuous logic; metric groups; unitary representations; amenable groups.
Continuous logic; metric groups; unitary representations; amenable groups.
Summary:
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 (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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