. We prove a jump inversion theorem for the enumeration jump and a minimal pair type theorem for the enumeration reducibilty. As an application some results of Selman, Case and Ash are obtained.

We show that the e-degree 0'e and the map u ↦ u' are definable in the upper semilattice of all e-degrees. The class of total e-degrees ≥0'e is also definable.