Project Euclid

We consider fine hierarchies in recursion theory, descriptive set theory, logic and complexity theory. The main results state that the sets of values of different Boolean terms coincide with the levels of suitable fine hierarchies. This gives new short descriptions of these hierarchies and shows that collections of sets of values of Boolean terms are almost well ordered by inclusion. For the sake of completeness we mention also some earlier results demonstrating the usefulness of fine hierarchies.