The problem of Common Knowledge will be considered in two classes of models: a class K.* of Kripke models and a class S of Scott models. Two modal logic systems will be defined. Those systems, KC and MC, include an axiomatisation of Common Knowledge. We prove determination of each system by the corresponding class of models. MSC: 03B45, 68T25.

We investigate an axiomatization of the notion of common belief that makes use of no rules of inference and highlight the property of the set of accessibility relations that characterizes each axiom.