Metric groups, unitary representations and continuous logic

Abstract

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 {\bf (T)} can be viewed as a union of first-order axiomatizable classes. We will see when these properties are preserved under taking elementary substructures.

15 pages; to appear in Communications in Mathematics, special issue "Ostrava seminar on Mathematical Physics". arXiv admin note: substantial text overlap with arXiv:1706.04157

References in corpus (6)

• Model theoretic forcing in analysis
• On Følner sets in topological groups
• Enforceable operator algebras
• Locally compact groups which are separably categorical structures
• Actions of metric groups and continuous logic
• On the nonexistence of Følner sets