Mathematical Sciences: Recursion Theory

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Stob will continue his work in recursion theory, a branch of mathematical logic which formalizes the notion of computability. He intends to study the structure of the lattice of recursively enumerable sets and the upper semilattice of recursively enumerable degrees. In particular, Stob will attempt to settle conjectures about orbits under automorphisms of the lattice of recursively enumerable sets, automorphism types of splittings of creative sets, and isomorphism types of lattices of supersets of r.e. sets. Stob will also attempt to answer questions about the Turing degrees of various natural classes of r.e. sets and will attempt to settle two questions about minimal pairs in the r.e. Turing degrees.