Generic sets and minimal $\alpha$-degrees
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- by C. T. Chong PDF
- Trans. Amer. Math. Soc. 254 (1979), 157-169 Request permission
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 $0’$.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- 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