Abstract
We prove that there are strong minimal pairs in the enumeration degrees and that the degrees of the left and right sides of strong minimal pairs include Σ20 degrees, although it is unknown if there is a strong minimal pair in the Σ20 enumeration degrees. We define a stronger type of minimal pair we call a strong super minimal pair, and show that there are none of these in the enumeration degrees, answering a question of Lempp et al. [6]. We leave open the question of the existence of a super minimal pair in the enumeration degrees.
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