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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Generic sets and minimal $ \alpha $-degrees


Author: C. T. Chong
Journal: Trans. Amer. Math. Soc. 254 (1979), 157-169
MSC: Primary 03D60; Secondary 03D30
MathSciNet review: 539912
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Abstract: A non-$ \alpha $-recursive subset G of an admissible ordinal $ \alpha $ is of minimal $ \alpha $-degree if every set of strictly lower $ \alpha $-degree than that of G is $ \alpha $-recursive. We give a characterization of regular sets of minimal $ \alpha $-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 $ \aleph _\omega ^L$-degree below $ 0'$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0539912-0
PII: S 0002-9947(1979)0539912-0
Keywords: Admissible ordinal, minimal $ \alpha $-degree, generic set
Article copyright: © Copyright 1979 American Mathematical Society