 Different versions of this theorem result from different constraints \(C(\sim)\) on the equivalence relation \(\sim\) (van Fraassen 1983; Shimony 1988), but the result is not surprising. An agent will satisfy Possibility of Vindication just in case her credences match the relative frequencies at some world. And those relative frequencies will satisfy the probability axioms if \(C(\sim)\) and if we have specified that condition correctly. That they will be rational numbers follows from the definition of the relative frequency of a proposition at a world.