Robert Soare Paul Snowden Russell Distinguished Service Professor Emeritus, Departments of Mathematics and Computer Science
My main research area is mathematical logic, especially the theory of recursive (i.e., computable) functions. I am studying the properties of recursively enumerable (r.e.) sets (those which can be generated by a computable procedure), particularly their algebraic structure, the degree of information they encode (Turing degree), their automorphisms, and their computational complexity properties. I am also working on the computable content of certain algebraic structures such as Boolean algebras and models of certain formal systems. Finally I am studying decision procedures for certain subclasses of the r.e. Turing degrees.