On the separability of elements and sets in hypergraphs of models of a theory

Abstract

We consider topological properties of hypergraphs of models of a theory. The separability of elements in these hypergraphs is characterized in terms of algebraic closures. Similarly we specify the separability of sets by the hypergraphs. The separability of finite sets is characterized for special hypergraphs defined by limit models as well as by countable models which are neither almost prime nor limit.