Relationships between NP-sets, Co-NP-sets, and P-sets relative to random oracles

@inproceedings{Vereshchagin1993RelationshipsBN,
title={Relationships between NP-sets, Co-NP-sets, and P-sets relative to random oracles},
author={Nikolai K. Vereshchagin},
booktitle={Structure in Complexity Theory Conference},
year={1993}
}

In the present paper we prove that relative to random oracle A (with respect to the uniform measure) the following three assertions hold: (1) there is a pair of disjoint NP A-sets which are separable by no P A-set, (2) there is a pair of disjoint Co-NP A-sets which are separable by no P A-set and (3) there is an innnite Co-NP A-set having no innnite NP A-subset

the property \A 2 U ) A 0 2 Indeed, let A 2 U. Let us prove that A 0 2 U. As C l doesn't belong to the set fB 1 ; : : :; B j g, the oracle A 0 is in ? m