Model-theoretic properties of regular polygons

A. V. Mikhalev ; E. V. Ovchinnikova ; E. A. Palyutin ; A. A. Stepanova

Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 107-157.

Résumé

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.

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