1-Generic splittings of computably enumerable degrees

Annals of Pure and Applied Logic 138 (1):211-219 (2006)
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Abstract

Say a set Gω is 1-generic if for any eω, there is a string σG such that {e}σ↓ or τσ↑). It is known that can be split into two 1-generic degrees. In this paper, we generalize this and prove that any nonzero computably enumerable degree can be split into two 1-generic degrees. As a corollary, no two computably enumerable degrees bound the same class of 1-generic degrees

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10.1016/j.apal.2005.06.012

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References found in this work

Double Jumps of Minimal Degrees.Carl G. Jockusch & David B. Posner - 1978 - Journal of Symbolic Logic 43 (4):715 - 724.
Minimal degrees and the jump operator.S. B. Cooper - 1973 - Journal of Symbolic Logic 38 (2):249-271.
Minimal degrees recursive in 1-generic degrees.C. T. Chong & R. G. Downey - 1990 - Annals of Pure and Applied Logic 48 (3):215-225.
The degrees below a 1-generic degree $.Christine Ann Haught - 1986 - Journal of Symbolic Logic 51 (3):770 - 777.

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