Embedding Logics into Product Logic

We construct a faithful interpretation of Lukasiewicz's logic in the product logic (both propositional and predicate). Using known facts it follows that the product predicate logic is not recursively axiomatizable. We prove a completeness theorem for the product logic extended by a unary connective 4 of Baaz 1]. We show that GG odel's logic is a sublogic of this extended product logic. We also prove NP-completeness of the set of propositional formulas satissable in product logic (resp. in GG odel's logic).