Some Descriptive-Set-Theoretical Problems in Complexity Theory

Abstract

We bring some descriptive-set-theoretical problems into complexity theory. We here deal with the uniformization problem and the separation problem. It is shown that 1) there exists an oracle A such that for some set S∈P[A] the uniformizator U_s is not in NP[A], 2) there is an oracle A such that Sep (NP[A]) does not hold and hence so does not Unif (coNP[A]), and 3) there is an oracle A such that Sep(NEXT [A]) does not hold and hence so does not Unif(coNEXT [A]).