Locally compact groups and continuous logic

TL;DR

This paper explores the capabilities of continuous logic in analyzing locally compact groups, focusing on their model-theoretic properties and characterizations of separably categorical groups.

Contribution

It advances understanding of how continuous logic applies to locally compact groups and characterizes those that are separably categorical.

Findings

Identification of classes of locally compact groups with specific logical properties

Characterization of separably categorical locally compact groups

Insights into the expressive power of continuous logic for group structures

Abstract

We study expressive power of continuous logic in classes of (locally compact) groups. We also describe locally compact groups which are separably categorical structures.