Bi-Isolation in the D.C.E. Degrees

Journal of Symbolic Logic 69 (2):409 - 420 (2004)
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
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DOI 10.2307/30041734
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Guohua Wu (2007). Intervals Containing Exactly One Ce Degree. Annals of Pure and Applied Logic 146 (1):91-102.

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