We bring some descriptive-set- theoretical problems into complexity theory. We here deal with the imiformization 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, 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]).
Cite this article
Hisao Tanaka, Some Descriptive-Set-Theoretical Problems in Complexity Theory. Publ. Res. Inst. Math. Sci. 28 (1992), no. 4, pp. 603–614DOI 10.2977/PRIMS/1195168210