In Jech's SET THEORY (a very early edition to which I have access), it is shown that the existence of 0-sharp implies the existence of a truth definition for the constructible universe L. Does the converse hold? I ask this question because in Koepke's paper "Turing Computations on Ordinals", he defines an ordinal computable "bounded truth predicate" (at least as I understand it, and I possibly don't understand it correctly) for each stage L_i of the constructible universe L. Are these two notions (0-sharp and Koepke's bounded truth predicate) at all related, and if so, in what way? At first glance (to me, at least) they seem to be because in Jech's text, the satisfaction relation is defined for each stage L_i of the hierarchy for L, just as the satisfaction relation seems so defined for Koepke's bounded truth predicate.