A Minimal Pair in the Generic Degrees

by Denis R. Hirschfeldt

Status: published in the Journal of Symbolic Logic 85 (2020) 531 - 537

Availability: journal version and preprint

Abstract. We show that there is a minimal pair in the nonuniform generic degrees, and hence also in the uniform generic degrees. This fact contrasts with Igusa's result that there are no minimal pairs for relative generic computability, and answers a basic structural question mentioned in several papers in the area.