Generic sets and minimal -degrees

Author:
C. T. Chong

Journal:
Trans. Amer. Math. Soc. **254** (1979), 157-169

MSC:
Primary 03D60; Secondary 03D30

DOI:
https://doi.org/10.1090/S0002-9947-1979-0539912-0

MathSciNet review:
539912

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Abstract | References | Similar Articles | Additional Information

Abstract: A non--recursive subset *G* of an admissible ordinal is of minimal -degree if every set of strictly lower -degree than that of *G* is -recursive. We give a characterization of regular sets of minimal -degree below 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 -degree below .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0539912-0

Keywords:
Admissible ordinal,
minimal -degree,
generic set

Article copyright:
© Copyright 1979
American Mathematical Society