Every Set has a Least Jump Enumeration

Richard J. Coles, Rod G. Downey, Theodore A. Slaman
2000 Journal of the London Mathematical Society  
Given a computably enumerable set B, there is a Turing degree which is the least jump of any set in which B is computably enumerable, namely 0 . Remarkably, this is not a phenomenon of computably enumerable sets. We show 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 Σ 0 1 (X).
doi:10.1112/s0024610700001459 fatcat:thdvs2ryvzdvnhjpmkgdbz2s4i