Mathematical Sciences: Recursive Function Theory

经典递归函数理论起源于一个 算法可计算概念的形式化。 最终，集合族中出现了丰富的结构， 自然地从这种形式主义中产生。 罗伯特·索尔将继续 研究递归函数理论的几个领域，包括 递归可重数（r.e.）图灵 度，r.e.的晶格。集合和度的属性 r.e.的差异集（d.r.e.）集. 他将探索 的连续性、可定义性和模型理论性质， r.e.结构度及其代数 结构和可能的自同构。 他将和拉克伦一起学习 D.R.E.的结构度和度的模型 算术 Soare将研究代数结构， 自同构和r.e.格的初等理论。集. 他还将研究某些代数的递归内容 结构，以确定哪些信息必须编码 它们的经典同构类型。

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.