SOME QUESTIONS OF UNIFORMITY IN ALGORITHMIC RANDOMNESS

The SI numbers the halting probabilities of universal prefix-free machines are known to be exactly the Martin-Lof random left-c.e. reals. We show that one cannot uniformly produce, from a Martin-L5f random left-c.e. real a, a universal prefix-free machine U whose halting probability is a. We also answer a question of Barmpalias and Lewis-Pye by showing that given a left-c.e. real a, one cannot uniformly produce a left-c.e. real 13 such that a 13 is neither left-c.e. nor right-c.e.