Quasiminimal structures, groups and Zariski-like geometries

TL;DR

This paper extends Hrushovski's Group Configuration Theorem to quasiminimal classes, introduces Zariski-like structures, and demonstrates the existence of groups in these structures when the associated pregeometry is non-trivial.

Contribution

It generalizes key theorems to quasiminimal classes and introduces Zariski-like geometries with new group existence results.

Findings

Group can be found in Zariski-like structures with non-trivial pregeometry

Generalization of Hrushovski's Group Configuration Theorem

Introduction of Zariski-like geometries

Abstract

We generalize Hrushovski's Group Configuration Theorem to quasiminimal classes. As an application, we present Zariski-like structures, a generalization of Zariski geometries, and show that a group can be found there if the pregeometry obtained from the bounded closure operator is non-trivial.