On structures in hypergraphs of models of a theory

Abstract

Hypergraphs of models of a theory are derived objects allowing toobtain an essential structural information about both giventheories and related semantic objects including graph ones. In the present paper we define and study structural properties of hypergraphs of modelsof a theory including lattice ones. Characterizations for thelattice properties of hypergraphs of models of a theory, as wellas for structures on sets of isomorphism types of models of atheory, are given.