2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218170We 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 the T-degrees below 0' for which there is a low T-upper bound.The second version repairs the details of one argument and makes other minor correctionsLogic03D15; 68Q30text