ON HYPERGRAPHS OF MINIMAL AND PRIME MODELS OF THEORIES OF ABELIAN GROUPS

被引：1

作者：

Sudoplatov, Sergey Vladimirovich ^{[1
,2
,3
]}

机构：

[1] Sobolev Inst Math, 4 Academician Koptyug Ave, Novosibirsk 630090, Russia

[2] Novosibirsk State Tech Univ, 20 K Marx Ave, Novosibirsk 630073, Russia

[3] Novosibirsk State Univ, 1 Pirogova Str, Novosibirsk 630090, Russia

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2020年 / 17卷

关键词：

hypergraph of models; minimal model; prime model; abelian group; elementary theory;

D O I：

10.33048/semi.2020.17.086

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We systematize known results about minimal and prime models of theories of abelian groups. Based on these results we describe properties and provide structural ones on hypergraphs of models for theories of abelian groups. In particular, we characterize non-emptiness and infiniteness of hypergraphs of minimal and prime models. We give necessary and sufficient conditions for almost disjointness of the respective hypergraphs. We also characterize conditions of preservation for non- emptiness and disjointness of hypergraphs of minimal and prime models at transformations to direct sums of groups.

引用

页码：1137 / 1154

页数：18

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