Fuzzy logic in narrow sense; Lukasiewicz logic; fuzzy theory; model theory of fuzzy logic; fuzzy logic with evaluated syntax

This paper is a contribution to the development of the model theory of fuzzy logic in narrow sense with evaluated syntax. Several generalizations of the concept of submodel are defined which have no counterpart in classical logic and demonstrate some properties of them. The main results concern elementary extensions and elementary chains. As a consequence, we will also present a generalization of the well known Craig's interpolation theorem for fuzzy logic.