Cut-free common knowledge

Starting off from the infinitary system for common knowledge over multi-modal epistemic logic presented in [L. Alberucci, G. Jäger, About cut elimination for logics of common knowledge, Annals of Pure and Applied Logic 133 (2005) 73–99], we apply the finite model property to “finitize” this deductive system. The result is a cut-free, sound and complete sequent calculus for common knowledge.