A basis result for Σ⁰₃ sets of reals with an application to minimal covers

Harrington, Leo A.; Kechris, Alexander S.

doi:10.1090/S0002-9939-1975-0398832-7

A basis result for $\Sigma \sp{0}\sb{3}$ sets of reals with an application to minimal covers

Authors: Leo A. Harrington and Alexander S. Kechris
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
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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.

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