 The condition that \(\omega \in \mathbf{K}_{i_1}\mathbf{K}_{i_2} \ldots \mathbf{K}_{i_m}(A)\) for all \(m \ge 1\) and all \(i_1, i_2 , \ldots ,i_m \in N\) is Schiffer’s definition of common knowledge, and is often used as the definition of common knowledge in the literature.