RESTRICTED JUMP INTERPOLATION IN THE D.C.E. DEGREES

It is shown that for any 2-computably enumerable Turing degree l, any computably enumerable degree a, and any Turing degree s, if l ′ = 0 ′, l < a, s ≥ 0 ′ , and s is c.e. in a, then there is a 2-computably enumerable degree x with the following properties: (1) l < x < a, and (2) x ′ = s.