Add to ORKGAbstract. Every K-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Martin-Löf random set that does not compute the halting problem. A major objective in algorithmic randomness is to understand how random sets and computably enumerable (c.e.) sets interact within the Turing degrees. At some level of randomness all interesting interactions cease. The lower and upper cones of noncomputable c.e. sets are definable null sets, and thus if a set is “sufficiently” random, it cannot compute, nor be computed by, a noncomputable c.e. set. How-ever, the most studied notion of algorithmic randomness, Martin-Löf randomness, is not strong enough to support this argument, and in fact, significant interactions between Martin-Lo...