Locally compact groups which are separably categorical structures

Abstract

We describe locally compact groups which are separably categorical metric structures.

Actions of metric groups and continuous logic

“…Note that the continuous logic approach takes weaker assumptions on d. Along with completeness it is only assumed that the operations of a structure are uniformly continuous with respect to d. Thus it is worth noting here that any group which is a continuous structure has an equivalent bi-invariant metric. See [15] for a discussion concerning this observation.…”