Genericity and Non-bounding in the Enumeration degrees

The structure of the semi lattice of enumeration degrees has been investigated from many aspects. One aspect is the bounding and non-bounding properties of generic degrees. Copestake proved that every 2-generic enumeration degree bounds a minimal pair and conjectured that there exists a 1-generic degree that does not bound a minimal pair. In this paper we verify this longstanding conjecture by constructing such a degree using an infinite injury priority argument.