Locally compact groups which are separably categorical structures

TL;DR

This paper characterizes locally compact groups that can be described as separably categorical metric structures, extending and correcting previous work in the area of continuous logic applied to group theory.

Contribution

It provides a detailed classification of locally compact groups within the framework of separably categorical metric structures, refining earlier results.

Findings

Identification of conditions for local compactness and separable categoricity

Extension and correction of previous classification results

Enhanced understanding of the model-theoretic properties of locally compact groups

Abstract

We describe locally compact groups which are separably categorical metric structures. The paper extends (and corrects) Section 3 of the paper A.Ivanov, "Locally compact groups and continuous logic", arXiv: 1206.5473