Ruling out certain configurations of beliefs constitute substantive assumptions about the players’ reasoning during the decision making process. In other words, substantive assumptions are about how, and how much, information is imparted to the agents, over and above those that are intrinsic to the mathematical formulation of the structures used to describe the players’ information. It is not hard to see that one always finds substantive assumptions in finite structures: Given a countably infinite set of atomic propositions, for instance, in finite structures it will always be common knowledge that some logically consistent combination of these basic facts are not realized, and a fortiori for logically consistent configurations of information and higher-order information about these basic facts. On the other hand, monotonicity of the belief/knowledge operator is a typical example of an assumption that is not substantive. More generally, there are no models of games, as we defined in Section 2, where it is not common knowledge that the players believe all the logical consequences of their beliefs.[19]