We show that there is a low T-upper bound for the class of K-trivial sets, namely those which are weak from the point of view of algorithmic randomness. This result is a special case of a more general characterization of ideals in Δ02 T-degrees for which there is a low T-upper bound.
"Low upper bounds of ideals." J. Symbolic Logic 74 (2) 517 - 534, June 2009. https://doi.org/10.2178/jsl/1243948325