A second step toward the polynomial hierarchy

Some of the questions posed by Baker, Gill, and Solovay [1] are here answered. The principal result is that there exists a recursive oracle for which the relativized polynomial hierarchy exists through the second level; that is, there is a recursive set B such that Σ2P,B ≠ π2P,B. It follows that Σ2P,B ⊂≠ Σ3P,B.