Mathematical Sciences: Recursion Theory

Lempp将继续研究经典递归理论。 他计划集中研究哪些结构可以 嵌入到图灵度的子类中（特别是 递归可重复度，其间隔，以及 递归可重复集的差度） 研究这些子类的代数结构， 他们的一阶理论片段的可判定性。 此外，他设想了一个新的优先权论证框架 类似于集合论中的强迫框架。 他总算 计划研究递归可重复集合的分裂。 递归理论处理的是 可计算性 它对我们如何 数学家思考证明的概念， 数学的核心概念。

Lempp will pursue research in classical recursion theory. He plans to concentrate on the question of which structures can be embedded into subclasses of the Turing degrees (in particular the recursively enumerable degrees, intervals thereof, and the degrees of differences of recursively enumerable sets) in order to study the algebraic structure of these subclasses as well as the decidability of fragments of their first-order theories. Furthermore, he envisions a new framework for priority arguments similar to the forcing framework in set theory. Finally, he plans to study splittings of recursively enumerable sets. Recursion theory deals with the theoretical limits of computability. It has had a profound effect on how mathematicians think about the notion of proof as well as other concepts at the core of mathematics.