 In addition to an axiomatization, Reichenbach attempts to provide a foundation for probability claims in terms of properties of sequences, similar to von Mises. Reichenbach regarded von Mises attempt (von Mises 1919) at formally characterizing a “random sequence” as a failure and instead attempted to characterize a weaker sequence property—a “normal” sequence. In his account of normal sequences Reichenbach retains (although the second only in a weaker form) two features that are deemed essential for random sequences: the lack of “after-effect” and the invariance of the limiting relative frequency under subsequence selection. Informally, the “invariance under subsequence selection” is supposed to capture the idea that the probabilities of events in any infinite subsequence selected from the original sequence by a procedure based on the indices of events in the original sequence alone will be the same as the probabilities of events in the original sequence. “The lack of aftereffect” is supposed to capture the idea that given any initial segment of a sequence, one cannot predict the probability of the next event any better than predicting it based on the limiting relative frequency of events in the infinite sequence. Reichenbach’s definition of lack of aftereffect is not based on initial segments of sequences, but rather on subsequences selected by a particular set of rules (1949f, p. 142). Reichenbach defines a “selection” S as any rule that determines for each member of a sequence whether it is a member of S (p. 143). He intends by a “rule” literally any subsequence. 