In this paper, we study the bi-isolation phenomena in the d.c.e. degrees and prove that there are c.e. degrees c1 < c2 and a d.c.e. degree d∈ (c1, c2) such that (c1, d) and (d, c2) contain no c.e. degrees. Thus, the c.e. degrees between c1 and c2 are all incomparable with d. We also show that there are d.c.e. degrees d1 < d2 such that (d1, d2) contains a unique c.e. degree.
"Bi-isolation in the d.c.e. degrees." J. Symbolic Logic 69 (2) 409 - 420, June 2004. https://doi.org/10.2178/jsl/1082418534