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Abstract
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 Hajek and Cintula (J Symb Log 71(3):863---880, 2006, Conjectures 1 and 2). We investigate also the properties of elementary extensions in witnessed and quasi-witnessed theories, generalizing some results of Section 7 of Hajek and Cintula (J Symb Log 71(3):863---880, 2006) and of Section 4 of Cerami and Esteva (Arch Math Log 50(5/6):625---641, 2011) to non-exhaustive models.
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