Slaman is engaged in several projects designed to illuminate the dynamic feature of computation, the structure of computable sets and the connection between notions of computability in varying environments. He plans separate studies in fragments of arithmetic; Turing degrees, global and local questions; recursion in higher types; and complexity theory. Investigations of this nature concern an idealized form of computing unlimited by memory size or practical time constraints. Positive results in this context may not be practically meaningful, but negative results, of course, are still perfectly meaningful. They constitute impossibility proofs in the very strong sense that even unreasonably huge memory and unreasonably lengthy computation runs will not suffice.
