NP-sets are Co-NP-immune relative to a random oracle

We prove that the class NP has Co-NP-immune sets relative to a random oracle. Moreover, we prove that, relative to a random oracle, there are L/spl isin/P and NP-set L/sub 1//spl sub/L such that both L/sub 1/ and L|L/sub 1/ are infinite, L/sub 1/ has no infinite Co-NP-subsets and L|L/sub 1/ has no infinite NP-subsets. The second theorem implies both the first theorem and the theorem in Vereshchagin (1993) that Co-NP has NP-immune sets relative to a random oracle.<>