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

Keywords:

d.c.e. degree; c.e. degree; bi-isolation
Full Text:

References:

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