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

Wang, Wei

J. Symb. Log. 76, No. 3, 897-913 (2011).

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

References:

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