Canonical and existential groups in universal classes of Abelian groups


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Resumo

Universal classes of Abelian groups are classified in terms of sets of finitely generated groups closed with respect to the discrimination operator. The notions of a principal universal class and a canonical group for such a class are introduced. For any universal class K, the class Kec of existentially closed groups generated by the universal theory of K is described. It is proved that Kec is axiomatizable and, therefore, the universal theory of K has a model companion.

Sobre autores

A. Mishchenko

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch

Autor responsável pela correspondência
Email: alexei.mishenko@gmail.com
Rússia, ul. Pevtsova 13, Omsk, 644099

V. Remeslennikov

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch; Omsk State Technical University

Email: alexei.mishenko@gmail.com
Rússia, ul. Pevtsova 13, Omsk, 644099; pr. Mira 11, Omsk, 644050

A. Treier

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch

Email: alexei.mishenko@gmail.com
Rússia, ul. Pevtsova 13, Omsk, 644099

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