The part about there being sets of infinitely many mutually exclusive hypotheses needs to be marked as an assumption, since I can construct languages where it does not hold. Also, you need to strengthen this assumption by saying that every hypothesis is part of at least one such set.
You also need to somehow get from “the probability of a statement decreases monotonically with its complexity” to “the probability of a statement decreases exponentially with its complexity”.
The part about there being sets of infinitely many mutually exclusive hypotheses needs to be marked as an assumption, since I can construct languages where it does not hold. Also, you need to strengthen this assumption by saying that every hypothesis is part of at least one such set.
You also need to somehow get from “the probability of a statement decreases monotonically with its complexity” to “the probability of a statement decreases exponentially with its complexity”.