Denis Hirschfeldt (University of Chicago)

May 19, 2020 @ 10:00 am – 11:00 am

Title: Minimal pairs in the generic degrees
by Denis Hirschfeldt (University of Chicago) as part of Computability theory and applications

Generic computability is a notion of “almost everywhere computability” that has been studied from a computability-theoretic perspective by several authors following work of Jockusch and Schupp. It leads naturally to a notion of reducibility, and hence to a degree structure. I will discuss the construction of a minimal pair in the generic degrees, which contrasts with Igusa’s result that there are
no minimal pairs for the similar notion of relative generic computability. I will then focus on several related questions that remain open.