Complexes of relational structures and their properties

We introduce the notion of a complex of relational structures, which is a new structure satisfying certain conditions with respect to the given finite collection of relation structures. We study some of its model-theoretic properties in relation with base structures, and show that, mostly, in order for the complex to have some property it should be generated by structures having given property. Furthermore, we introduce the notion of finitely equivalent sets of the structure, and based on it introduce properties of regularity, strictness, and properness, that allow us to guarantee that the complex generated by a collection of structures having сertain model-theoretic properties will also have these properties. We show that the structure of the complex and its properness and strictness are preserved under expansions of the structure by new relations satisfying сertain conditions.