A basis result for $\Sigma ^{0}_{3}$ sets of reals with an application to minimal covers
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- by Leo A. Harrington and Alexander S. Kechris
- Proc. Amer. Math. Soc. 53 (1975), 445-448
- DOI: https://doi.org/10.1090/S0002-9939-1975-0398832-7
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Abstract:
It is shown that every $\Sigma _3^0$ set of reals which contains reals of arbitrarily high Turing degree in the hyperarithmetic hierarchy contains reals of every Turing degree above the degree of Kleene’s $\mathcal {O}$. As an application it is shown that every Turing degree above the Turing degree of Kleene’s $\mathcal {O}$ is a minimal cover.References
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Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 445-448
- MSC: Primary 02K30; Secondary 02F30, 04A15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0398832-7
- MathSciNet review: 0398832