In this paper we study generic expansions of predicate logics of some left-continuous t-norms (mainly Gödel and Nilpotent Minimum predicate logics) with a countable set of truth-constants. Using known results on tnorm based predicate fuzzy logics we obtain results on the conservativeness and completeness for the expansions of some predicate fuzzy logics. We describe the problem for the cases of Lukasiewicz and Product predicate logics and prove that the expansions of Gödel and Nilpotent Minimum

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... predicate logics are canonical complete for tautologies, and strong standard complete for deduction upon any set of premisses.