Constant compression and random weights

Wolfgang Merkle & Jason Teutsch
Omega numbers, as considered in algorithmic randomness, are by definition real numbers that are equal to the halting probability of a universal prefix-free Turing machine. Omega numbers are obviously left-r.e., i.e., are effectively approximable from below. Furthermore, among all left-r.e. real numbers in the appropriate range between 0 and 1, the Omega numbers admit well-known characterizations as the ones that are Martin-Löf random, as well as the ones such that any of their effective approximation...