We prove that there is a Δ₂⁰, 1-random set Y such that every computably enumerable set which is computable from Y is strongly jump-traceable.
We also show that for every order function h there is an ω-c.e. random set Y such that every computably enumerable set which is computable from Y is h-jump-traceable. This establishes a correspondence between rates of jump-traceability and computability from ω-c.e. random sets.
Noam Greenberg. "A random set which only computes strongly jump-traceable c.e. sets." J. Symbolic Logic 76 (2) 700 - 718, June 2011. https://doi.org/10.2178/jsl/1305810771