{"docId":9526,"paperId":9526,"url":"https:\/\/cm.episciences.org\/9526","doi":"10.2478\/cm-2021-0007","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":647,"name":"Volume 29 (2021), Issue 1 (Special Issue: Ostrava Mathematical Seminar)"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-03665007","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-03665007v1","dateSubmitted":"2022-05-11 15:42:24","dateAccepted":null,"datePublished":"2021-04-30 00:00:00","titles":{"en":"Metric groups, unitary representations and continuous logic"},"authors":["Ivanov, Aleksander"],"abstracts":{"en":"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\u03c9 1 \u03c9 -axiomatization of amenability. We also show that in the case of locally compact groups some uniform version of the negation of Kazhdan\u2019s 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."},"keywords":[["General Mathematics"],"[MATH]Mathematics [math]"]}