In this paper, we present Carnap’s modal logic C, which is one of the first attempts to use the concept of possible world in shaping the semantics for modalities. Some older technical results, which concern the logic C, are summarized, namely two different kinds of axiomatization of C, one unusual characterization of C as the only set of formulae having one special property, and semantical and syntactical relations of C to S5. The fact that C is not closed under the (...) universal substitution is shortly discussed. Finally, the predicate version of C, which is not axiomatizable, is defined. (shrink)