Douglas Cenzer (Gainesville)
Structures and Isomorphisms in the Difference Hierarchy

This will include recent work on injection structures and on structures with functions f which are at most two-to-one. Such structures consist of orbits, where the orbit of a point a is the set of all elements x such that either f n(x) = a or f n(a) = x, for some n. A central goal is to characterize structures which are computably categorical or more generally Δ 02 categorical. The universe of a structure may be a computable set, or a c.e. set, or more generally, an n-c.e. set, where an element may go into and back out of the universe multiple times. We also consider functions which may change a finite number of times, as well as isomorphisms which may change.

Please consider that this abstract may also change a finite number of times.