  An algebraic setting for the validity of Pavelka style completeness for some
natural expansions of \L ukasiewicz logic by new connectives and rational
constants is given. This algebraic approach is based on the fact that the
standard MV-algebra on the real segment $[0, 1]$ is an injective MV-algebra. In
particular the logics associated with MV-algebras with product and with
divisible MV-algebras are considered.
