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Bi-isolation in the d.c.e. degrees. (English) Zbl 1076.03028

In this paper the author investigates the bi-isolation phenomena in the d.c.e. degrees and proves that there are c.e. degrees \(c_1<c_2\) and a d.c.e degree \(d\in(c_1,c_2)\) such that \((c_1,d)\) and \((d,c_2)\) contain no c.e. degrees. Thus, the c.e. degrees between \(c_1\) and \(c_2\) are all incomparable with \(d\). It it also shown that there are d.c.e. degrees \(d_1<d_2\) such that \((d_1,d_2)\) contains a unique c.e. degree.

MSC:

03D25 Recursively (computably) enumerable sets and degrees
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References:

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