Almost universal cupping and diamond embeddings

In this paper, we study the cupping property in the d.r.e. degrees, and prove the existence of a d.r.e. degrees with almost universal cupping property and nonzero r.e. degrees and such that isolates in the d.r.e. degrees, and and form a minimal pair. As a corollary, we have that for any nonzero r.e. degree and incomplete d.r.e. degree , and form a diamond embedding in the d.r.e. degrees.