 If the probability function \(P\) is clear from the context, we will often simply write \(U\) instead of \(U_P\). In the remainder of this subsection (and in the next one as well) we will assume that all arguments have only finitely many premises (which is not a significant restriction, given the compactness property of classical propositional logic). Adams’ first main result, which was originally established by Suppes (1966), can now be stated as follows: