Iterated Relative
نویسندگان
چکیده
A result of Soare and Stob asserts that for any non-recursive r.e. set C, there exists a r.e.[C] set A such that A⊕C is not of r.e. degree. A set Y is called [of] m-REA (m-REA[C]) [degree] iff it is [Turing equivalent to] the result of applying m-many iterated ‘hops’ to the empty set (to C), where a hop is any function of the form X 7→ X ⊕W e . The cited result is the special case m = 0, n = 1 of our Theorem. For m = 0, 1, and any (m + 1)-REA set C, if C is not of m-REA degree, then for all n there exists a n-r.e.[C] set A such that A⊕C is not of (m+ n)-REA degree.
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