Sofic metric groups and continuous logic

TL;DR

This paper introduces various classes of metric groups such as sofic, weakly sofic, linear sofic, and hyperlinear, and explores their axiomatizability within continuous logic, advancing the theoretical understanding of these groups.

Contribution

It defines new classes of metric groups and investigates their logical axiomatizability, contributing to the foundational theory of metric group classes.

Findings

Defined new classes of metric groups including sofic and hyperlinear.

Discussed issues related to axiomatizability in continuous logic.

Explored theoretical properties of these classes.

Abstract

We define sofic, weakly sofic, linear sofic and hyperlinear metric groups and discuss some issues involving axiomatizability of these classes in continuous logic.