Universal test for Hippocratic randomness

Abstract: Hippocratic randomness is defined in a similar way to Martin-Lof randomness, however it does not assume computability of the probability and the existence of universal test is not assured. We introduce the notion of approximation of probability and show the existence of the universal test (Levin-Schnorr theorem) for Hippocratic randomness when the logarithm of the probability is approximated within additive constant.