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non-isolated degrees

Proceedings of the London Mathematical Society (1)

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On the density of the pseudo-isolated degrees
Guohua Wu
Journal:

Proceedings of the London Mathematical Society / Volume 88 / Issue 2 / March 2004

Published online by Cambridge University Press:

08 March 2004, pp. 273-288

Print publication:

March 2004
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A d.c.e. (2-computably enumerable) degree d is pseudo-isolated if d itself is non-isolated (in the sense that no computably enumerable (c.e.) degree below d can bound the c.e. degrees below d) and there is a d.c.e. degree \textbf{b} < \textbf{d} bounding all c.e. degrees below d. We prove in this paper that the pseudo-isolated degrees are densely distributed in the c.e. degrees.