## Relative enumerability and 1-genericity.(English)Zbl 1260.03079

Summary: A set of natural numbers $$B$$ is computably enumerable in and strictly above (or c.e.a. for short) another set $$C$$ if $$C <_{T} B$$ and $$B$$ is computably enumerable in $$C$$. A Turing degree $$\mathbf b$$ is c.e.a. $$\mathbf c$$ if $$\mathbf b$$ and $$\mathbf c$$ respectively contain $$B$$ and $$C$$ as above. In this paper, it is shown that if $$\mathbf b$$ is c.e.a. $$\mathbf c$$ then $$\mathbf b$$ is c.e.a. some 1-generic $$\mathbf g$$.

### MSC:

 03D28 Other Turing degree structures 03D25 Recursively (computably) enumerable sets and degrees

### Keywords:

Turing degrees; relative enumerability; 1-generic
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### References:

 [1] DOI: 10.1007/s00153-005-0306-y · Zbl 1148.03033 [2] Recursively enumerable sets and degrees (1987) [3] Relative recursive enumerability of generic degrees 56 pp 1075– (1991) · Zbl 0753.03017 [4] Bounding non-GL2 and r.e.a. 74 pp 989– (2009) [5] DOI: 10.1090/S0002-9939-1954-0063995-6 [6] DOI: 10.1016/0168-0072(93)90143-2 · Zbl 0805.03030 [7] Recursion theory: Its generalizations and applications, Proceedings of Logic Colloquium ’79, Leeds, August 1979 pp 110– (1980)
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