Transactions of the American Mathematical Society
We show that for every coinfinite r.e. set A there is a complete r.e. set B such that ℒ⋆(A)≈ ℒ⋆(B) and that every promptly simple set is automorphic (in f⋆) to a complete set.
Cholak, Peter; Downey, Rod G.; and Stob, Michael, "Automorphisms of the lattice of recursively enumerable sets: Promptly simple sets" (1992). University Faculty Publications. 464.