Hierarchies based on computational complexity and irregularities of class determining measured sets (Preliminary Report)
Leonard J. Bass, Paul R. Young · 1970
We consider here the problem of building transfinite hierarchies of computable functions on the basis of their difficulty of computation. Previous hierarchies of functions through the constructive ordinals have had two major problems, each apparently caused by not having techniques to restrict the classes considered at limit ordinals. These problems are, first that every function occurs at some name for ω, or some other small ordinal, and second that two names for the same constructive ordinal have two different classes of functions associated with them.