THE CHAIN METHOD TO SEPARATE COUNTING CLASSES

We introduce a new method to separate counting classes of a special ty pe by oracles. Among the classes, for which this method is applicable, are NP, coNP, US (also called 1-NP), +P, all other MOD-classes, PP, a nd C=P, classes of Boolean Hierarchies over the named classes, classes of finite acceptance type, and many more. As an important special cas e, we completely characterize all relativizable inclusions between cla sses NP(k) from the Boolean Hierarchy over NP and other classes define d by what we call bounded counting.