Bi-isolation in the d.c.e. degrees

Journal of Symbolic Logic 69 (2):409-420 (2004)
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Abstract

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∈ such that and 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 contains a unique c.e. degree.

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The d.r.e. degrees are not dense.S. Cooper, Leo Harrington, Alistair Lachlan, Steffen Lempp & Robert Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.
The Isolated D. R. E. Degrees are Dense in the R. E. Degrees.Geoffrey Laforte - 1996 - Mathematical Logic Quarterly 42 (1):83-103.
Isolation and the high/low hierarchy.Shamil Ishmukhametov & Guohua Wu - 2002 - Archive for Mathematical Logic 41 (3):259-266.
The density of the low2 n-r.e. degrees.S. Barry Cooper - 1991 - Archive for Mathematical Logic 31 (1):19-24.

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