Minimal pairs in initial segments of the recursively enumerable degrees (Q1366939)

Two degrees \textbf{a} and \textbf{b} form a minimal pair if \({\mathbf a}\cap {\mathbf b}= \mathbf{0}\). The degrees \textbf{a} and \textbf{b} are called halfs of the pair. The authors study the problem of describing the computably enumerable (c.e.) degrees forming a half of a minimal pair and show that in every lower cone bounded by a non-zero c.e. degree there is a degree which is not a half of a minimal pair (in the cone). This result is related to a result of the reviewer, who proved that there is a cone bounded by a c.e. degree in which every degree is a half of a minimal pair in a wider class of \(\omega\)-c.e. degrees.