Mathematical Sciences: Recursion Theory

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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.