Questions in recursion theory

1.3. (Slaman–Woodin Conjectures) (a) D is biinterpretable with second order arithmetic. In other words, the relation (on ~ p and d) “~ p codes a standard model of first order arithmetic and a real X such that X is of degree d” is definable in D. (b) Suppose that I is an ideal inD such that there is a 1-generic degree in I. Then I is biinterpretable with that fragment of second order arithmetic in which the real numbers are just those sets whose Turing degrees belong to I.