Model-theoretic properties of regular polygons

This work is devoted to results obtained in the model theory of regular polygons. We give a characterization of monoids with axiomatizable and model-complete class of regular polygons. We describe the monoids with complete class of regular polygons that satisfy some additional conditions. We study the monoids whose regular core is represented as a union of finitely many principal right ideals and all regular polygons over which have a stable and superstable theory. We prove the stability of the class of all regular polygons over a monoid provided this class is axiomatizable and model-complete. We also describe the monoids for which the class of all regular polygons is superstable and $\omega$-stable provided this class is axiomatizable and model-complete.