Canonical and existential groups in universal classes of Abelian groups
- Autores: Mishchenko A.A.1, Remeslennikov V.N.1,2, Treier A.V.1
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Afiliações:
- Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch
- Omsk State Technical University
- Edição: Volume 93, Nº 2 (2016)
- Páginas: 175-178
- Seção: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/223498
- DOI: https://doi.org/10.1134/S1064562416020149
- ID: 223498
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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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