Array Nonrecursive Degrees and Genericity
نویسندگان
چکیده
A class of r.e. degrees, called the array nonrecursive degrees, previously studied by the authors in connection with multiple permitting arguments relative to r.e. sets, is extended to the degrees in general. This class contains all degrees which satisfy a 00 > (a 0 0) 0 (i.e. a 2 GL 2) but in addition there exist low r.e. degrees which are array nonrecursive (a.n.r.). Many results for GL 2 degrees extend to the a.n.r. degrees and thus to certain low degrees. A new notion of genericity (called pb-genericity) is introduced which is intermediate between 1-genericity and 2-genericity. It is shown that the upward closure of the pb-generic degrees is the set of a.n.r. degrees.
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