 Reichenbach proceeds to show that finite frequencies satisfy his four axioms. He construes all probabilities as frequencies of sub-series in a larger series—or what is the same thing for finite sets, cardinalities of subsets in a universal set. Hence his probabilities are always with respect to a non-empty reference class, so the probability that an event is in a class B is in Reichenbach’s notation, P(A, B) where A is the reference class—similar to the modern notation of the conditional probability P(B | A). But the probability logic axioms are so weak that many formal structures satisfy them, and Reichenbach’s claim is a long way from a representation theorem. He fails to provide the additional constraints on the space that probabilities are applied to, which in Kolmogorov’s case are given by the assumption that the space is a sigma-field, i.e. a field closed under complementation and countable union. 