Canonical and existential groups in universal classes of Abelian groups
| Autor: | Vladimir N. Remeslennikov, A. A. Mishchenko, Alexander Treier |
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| Rok vydání: | 2016 |
| Předmět: |
Class (set theory)
Group (mathematics) General Mathematics 010102 general mathematics Amalgamation property 01 natural sciences Universal class Existentialism 010305 fluids & plasmas Combinatorics Torsion-free abelian group Operator (computer programming) 0103 physical sciences 0101 mathematics Abelian group Mathematics |
| Zdroj: | Doklady Mathematics. 93:175-178 |
| ISSN: | 1531-8362 1064-5624 |
| DOI: | 10.1134/s1064562416020149 |
| Popis: | 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 K ec of existentially closed groups generated by the universal theory of K is described. It is proved that K ec is axiomatizable and, therefore, the universal theory of K has a model companion. |
| Databáze: | OpenAIRE |
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