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.
Lismont, L. (1993). La connaissance commune en logique modale. Mathematical Logic Quarterly, 39(1), 115-130. https://doi.org/10.1002/malq.19930390114 (Original work published 1993)