Charles Harris

My research is in Computability Theory and centres on the first order properties of the degree structures of positive reducibilities, with a special focus on the Enumeration degree structure. The study of the Enumeration degrees is closely related to research in the Turing degrees, due to the similarity of its proof techniques and constructions, and because of the existence of a natural canonical embedding of the Turing degrees into the Enumeration degrees. It is also motivated by the fact that Enumeration reducibility has been shown to be the most general form of positive reducibility, and that the operators of Enumeration reducibility correspond to closed terms of the untyped Lambda Calculus under Scott's Graph Model interpretation of the latter.

I am also interested in complexity theory and specific issues concerning the computational properties of mathematical structures.