Categories of elementary sets over algebras and categories of elementary algebraic knowledge

For every variety of algebras Theta and every algebra H in Theta we consider the category of algebraic sets K-Theta(H) in Theta over H. We consider also the category of elementary sets LK Theta(H). The latter category is associated with a geometrical approach to the First Order Logic over algebras. It is also related to the category of elementary knowledge about algebra H. Grounding on these categories we formally introduce and study the intuitive notions of coincidence of algebraic geometries over algebras H-1 and H-2 from Theta, of coincidence of logics over H-1 and H-2, and of coincidence of the corresponding knowledge. This paper is a survey of ideas stimulated by this approach.