A model-theoretic note on the Freiman-Ruzsa theorem

TL;DR

This paper presents a non-quantitative version of the Freiman-Ruzsa theorem applicable to finite stable sets with small tripling in arbitrary groups and weakly normal subsets in abelian groups.

Contribution

It introduces a new non-quantitative perspective on the Freiman-Ruzsa theorem for specific classes of sets in groups.

Findings

Applicable to finite stable sets with small tripling

Extends to weakly normal subsets in abelian groups

Provides a non-quantitative version of the theorem

Abstract

A non-quantitative version of the Freiman-Ruzsa theorem is obtained for finite stable sets with small tripling in arbitrary groups, as well as for (finite) weakly normal subsets in abelian groups.