3 Pilar Dellunde Francesc Esteva 2010 E. Huellermeier, R. Kruse, and F. Hoffmann IPMU 2010 Dortmund, Germany 6178 747-756 Lecture Notes in Artificial Intelligence 28/06/2010 equality-free language, fuzzy predicate logic, model theory, elementary extension, elementary equivalence Abstract. Our work is a contribution to the model-theoretic study of equality-free fuzzy predicate logics. We give a characterization of ele- mentary equivalence in fuzzy predicate logics using elementary exten- sions and introduce an strengthening of this notion, the so-called strong elementary equivalence. Using the method of diagrams developed in [5] and elementary extensions we present a counterexample to Conjectures 1 and 2 of [8].