An Operator Embedding Theorem for Complexity Classes of Recursive Functions

Abstract

Let F (t) be the set of functions computable by some machine using no more than t(x) machine steps on all but finitely many arguments x. If we order the - classes under set inclusion as t varies over the recursive functions, then it is natural to ask how rich a structure is obtained. We show that this structure is very rich indeed. If R is any countable partial order and F is any total effective operator, then we show that there is a recursively enumerable sequence of...