On hypergraphs of minimal and prime models of theories of abelian groups

Abstract

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 inniteness of hypergraphs of minimal and prime models. We give necessary and sucient conditions for almost disjointness of the respective hypergraphs. We also characterize conditions of preservation for nonemptiness and disjointness of hypergraphs of minimal and prime models at transformations to direct sums of groups.