Pseudojumps and Formula Classes
Douglas Cenzer, Geoffrey Laforte, Guohua Wu · Journal of Logic and Computation · 2008
For a pseudojump VX and a Π10 class P, we consider properties of the set {VX:X ∈ P}.We show that if P is Medvedev complete or if P has positive measure, and Ø′ ≤T C, then there exists X ∈ P with VX ≡T C. We examine the consequences when VX is Turing incomparable with VY for X ≠ Y in P and when WeX=WeY for all X, Y ∈ P. Finally, we give a characterization of the jump in terms of Π10 classes.