Theoretic--model Properties of Regular Polygons

TL;DR

This paper investigates the model-theoretic properties of regular polygons over monoids, providing characterizations of classes with various stability and completeness properties.

Contribution

It offers a comprehensive characterization of monoids with axiomatizable, model complete, stable, and superstable classes of regular polygons, advancing the theoretical understanding.

Findings

Characterization of monoids with axiomatizable and model complete classes

Description of monoids with stable and superstable classes of regular polygons

Proof of stability for the axiomatizable model complete class

Abstract

This work is dedicated to the results were got in the model theory of the regular polygons. We give the characterization of the monoids with axiomatizable and model complete class of regular polygons. We describe the monoids with complete class of regular polygons which satisfy the additional conditions. We study the monoids, whose regular core is presented as a union of the finite number of principal right ideals, all regular polygons over which have the stable and superstable theory. We prove the stability of the axiomatizable model complete class of regular polygons and we also describe the monoids with the superstable and $\omega$--stable class of regular polygons when this class is axiomatizable and model complete.