In the last few decades many formal systems of fuzzy logics have
been developed. Since the main differences between fuzzy and
classical logics lie at the propositional level, the fuzzy predicate
logics have developed more slowly (compared to the propositional
ones). In this text we aim to promote interest in fuzzy predicate
logics by contributing to the model theory of fuzzy predicate
logics. First, we generalize the completeness theorem, then we use
it to get results on conservative extensions of theories and on
witnessed models.