 Informally, a proposition \(A\) is mutually known among a set of agents if each agent knows that \(A\). Mutual knowledge by itself implies nothing about what, if any, knowledge anyone attributes to anyone else. Suppose each student arrives for a class meeting knowing that the instructor will be late. That the instructor will be late is mutual knowledge, but each student might think only she knows the instructor will be late. However, if one of the students says openly “Peter told me he will be late again,” then the mutually known fact is now commonly known. Each student now knows that the instructor will be late, and so on, ad infinitum. The agents have common knowledge in the sense articulated informally by Schelling (1960), and more precisely by Lewis (1969) and Schiffer (1972). Schiffer uses the formal vocabulary of  epistemic logic  (Hintikka 1962) to state his definition of common knowledge. Schiffer’s general approach was to augment a system of sentential logic with a set of knowledge operators corresponding to a set of agents, and then to define common knowledge as a hierarchy of propositions in the augmented system. Bacharach (1992) and Bicchieri (1993) adopt this approach, and develop logical theories of common knowledge which include soundness and completeness theorems in the style of (Fagin et al. 1995). One can also develop formal accounts of common knowledge in set-theoretic terms, as it was done in the early Friedell (1969) and in the economic literature after Aumann (1976). Such an approach, easily proven to be equivalent to the ones cast in epistemic logic, is taken also in this  article.[8]