Minimal pairs in the generic degrees

Abstract: 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.

logic

Audience: researchers in the topic

Computability theory and applications

Series comments: Description: Computability theory, logic

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