Actions of metric groups and continuous logic

TL;DR

This paper explores the expressive capabilities of continuous logic when applied to classes of metric groups characterized by properties of their actions, extending previous foundational work in the field.

Contribution

It significantly advances understanding of how continuous logic can describe properties of metric groups, building on and extending prior research by Ivanov.

Findings

Extended the analysis of properties like non-OB, non-FH, and non-FR in metric groups.

Demonstrated the expressive power of continuous logic in classifying metric group actions.

Connected properties of metric groups with logical frameworks.

Abstract

We study expressive power of continuous logic in classes of metric groups defined by properties of their actions. For example we consider properties non-OB, non-FH and non-FR. The paper substantially extends Section 2 of the paper A.Ivanov, "Locally compact groups and continuous logic", arxiv:1206.5473.