Automorphisms of the lattice of recursively enumerable sets: promptly simple sets
Peter A. Cholak, Rodney G. Downey, Michael Stob · Transactions of the American Mathematical Society · 1992
We show that for every coinfinite r.e. set A A there is a complete r.e. set B B such that L ∗ ( A ) ≈ eff L ∗ ( B ) {\mathcal {L}^{\ast } }(A){ \approx _{{\text {eff}}}}{\mathcal {L}^{\ast } }(B) and that every promptly simple set is automorphic (in E ∗ {\mathcal {E}^{\ast } } ) to a complete set.