 Let \(W\) be the set of all possible worlds, \(F\) the function which assigns to each world \(w\) the set \(F_w\) of facts which exist in it, and \(F\) the union of all the \(F_w s\), i.e., the set of all facts. We assume that \(W\) has infinitely many members. This is a reasonable assumption, which will have some importance in what follows with respect to certain entailment claims we are going to make (not having the assumption would force us to distinguish cases). Since we are dealing with theories of facts, we shall also assume that \(F\) is non-empty. Although perhaps there are impossible states of affairs or situations, we take it that there are no impossible facts. That is why there is no room for them in our framework.