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Generic sets and minimal $\alpha $-degrees

1979
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Transactions of the American Mathematical Society
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A non-a-recursive subset G of an admissible ordinal a is of minimal a-degree if every set of strictly lower a-degree than that of G is a-recursive. We give a characterization of regular sets of minimal a-degree below 0' via the notion of genericity. We then apply this to outline some 'minimum requirements' to be satisfied by any construction of a set of minimal N -degree below 0'. In 1956 Spector [8] showed the existence of a minimal Turing degree. This result stimulated the study of initial

doi:10.1090/s0002-9947-1979-0539912-0
fatcat:ldhiaws3jfhankdstthxe6pdg4