 Proposition 2.17 (Aumann 1976)  Let \(\mathcal{M}\) be the meet of the agents’ partitions \(\mathcal{H}_i\) for each \(i \in N\). A proposition \(E \subseteq \Omega\) is common knowledge for the agents of \(N\) at \(\omega\) iff \(\mathcal{M}(\omega) \subseteq E\). (In Aumann (1976), \(E\) is defined to be common knowledge at \(\omega\) iff \(\mathcal{M}(\omega) \subseteq E\).)  Proof.