Weak recursive degrees and a problem of Spector - Semantic Scholar
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Abstract. We introduce a concept of weak recursive degrees and show that each weak recursive degree possess a strong minimal cover (s.m.c.). Since the class ...
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Weak recursive degrees and a problem of Spector - Semantic Scholar
of recursively enumerable degrees. A degree m is a strong minimal cover for a degree a, if a
In M.Arslanov and S. Lempp, editors, Recursion Theory and Complexity, Kazan, de Gruyter Series in Logic and Its Applications, v.2, Berlin, NewYork, 1999, pp.81-87
Weak recursive degrees and a problem of Spector Sh.T.Ishmukhanetov Abstract We introduce a concept of weak recursive degrees and show that each weak recursive degree possess a strong minimal cover (s.m.c.). Since the class of r.e. array nonrecursive (a.n.r.) degrees defined by Downey, Jockusch and Stob [1990] is complementary to the class of weak recursive degrees in the r.e. degrees R and no a.n.r.degree can possess a s.m.c. we obtain as a corollary that a r.e. degree possess a s.m.c. iff it is weak recursive. This gives a decision of Spector problem of description of degrees possessing strong minimal covers for the case of recursively enumerable degrees.
A degree m is a strong minimal cover for a degree a, if a
