Mathematical Sciences: Recursive Function Theory

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Classical recursive function theory arises from a formalization of the notion of algorithmically computable. Ultimately a rich structure appears in the family of sets that arise naturally from this formalism. Robert Soare will continue research in several areas of recursive function theory, including the structure of the recursively enumerable (r.e.) Turing degrees, the lattice of r.e. sets, and properties of degrees of differences of r.e. sets (d.r.e.) sets. He will explore continuity, definability, and model theoretic properties of the structure of the r.e. degrees as well as their algebraic structure and possible automorphisms. With Lachlan he will study the structure of the d.r.e. degrees and degrees of models of arithmetic. Soare will study the algebraic structure, automorphisms, and elementary theory of the lattice of r.e. sets. He will also study the recursive content of certain algebraic structures, to determine what information is necessarily coded into their classical isomorphism types.