Our work is a contribution to the model theory of fuzzy predicate logics. In this paper we characterize elementary equivalence between models of fuzzy predicate logic using elementary mappings. Refining the method of diagrams we give a solution to an open problem of P. Hájek and P. Cintula (Conjectures 1 and 2 of [HaCi06]). We investigate also the properties of elementary extensions in witnesse...
