Given a computably enumerable set W, there is a Turing degree which is the least jump of any set in which W is computably enumerable, namely 0′. Remarkably, this is not a phenomenon of computably enumerable sets. It is shown that for every subset A of ℕ, there is a Turing degree, c′μ(A), which is the least degree of the jumps of all sets X for which A is [sum ]01(X). In addition this result provides an isomorphism invariant method for assigning Turing degrees to certain torsion-free abelian groups.