  We study $[0,1]$-valued logics that are closed under the
{\L}ukasiewicz-Pavelka connectives; our primary examples are the the continuous
logic framework of Ben Yaacov and Usvyatsov \cite{Ben-Yaacov-Usvyatsov:2010}
and the {\L}ukasziewicz-Pavelka logic itself. The main result of the paper is a
characterization of these logics in terms of a model-theoretic property,
namely, an extension of the omitting types theorem to uncountable languages.
