 In combination with the representation of probability relations by claims in a quasilogical language, the limiting frequency interpretation creates fundamental formal problems that Reichenbach did not foresee. Sets of limiting relative frequencies are not closed under finite intersection; they are not closed under countable union; they do not satisfy countable additivity. They do not, in other words, form a sigma field, or a Borel field, or even a field. (See the entries on  interpretations of probability,  the early development of set theory, and  set theory.)  These and several other mathematical difficulties of Reichenbach’s setup are described in van Fraassen  (1979).[4] 