Relative enumerability and 1-genericity

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 b is c.e.a. c if b and c respectively contain B and C as above. In this paper, it is shown that if b is c.e.a. c then b is c.e.a. some 1-generic g.

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