Mathematical Sciences: Recursion Theory

Stob将继续他在递归理论方面的工作，递归理论是数学逻辑的一个分支，它形式化了可计算性的概念。他打算研究递归可枚举集格的结构和递归可枚举度的上半格。特别是，Stob将尝试解决关于递归可枚举集的格的自同构下的轨道的猜想，创造集的分裂的自同构类型，以及r.e.集的超集的格的同构类型。Stob还将尝试回答关于各种自然类别的r.e.集的图灵度的问题，并将尝试解决关于r.e.图灵度中的最小对的两个问题。

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.