# Some Descriptive-Set-Theoretical Problems in Complexity Theory

### Hisao Tanaka

Hosei University, Tokyo, Japan

## Abstract

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. 603–614

DOI 10.2977/PRIMS/1195168210