 Monderer and Samet (1988) and Binmore and Brandenburger (1989) give a particularly elegant set-theoretic definition of common knowledge. I will review this definition here, and then show that it is logically equivalent to the ‘\(i\) knows that \(j\) knows that \(\ldots k\) knows that A’ hierarchy that Lewis (1969) and Schiffer (1972) argue characterizes common  knowledge.[9]