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Metric groups, unitary representations and continuous logic
Communications in Mathematics, Tome 29 (2021) no. 1, pp. 35-48 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 03C52, 22F05
Keywords: Continuous logic; metric groups; unitary representations; amenable groups. 
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Ivanov, Aleksander. Metric groups, unitary representations and continuous logic. Communications in Mathematics, Tome 29 (2021) no. 1, pp. 35-48. http://geodesic.mathdoc.fr/item/COMIM_2021_29_1_a2/

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