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By Borel determinacy (exercisce XIII.1.7 in Odifreddi) there is a cone of minimal covers in the arithmetic degrees. Is the base of such a cone known? A minimal such base?

For that matter, is it even known if there is a minimal base of a cone of arithmetic minimal covers?

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  • $\begingroup$ I'd guess that by analogy with the Turing degree case that $0^{(\omega\cdot\omega)}$ would be the base of such a cone but I wouldn't be sure how to prove it since it's not obvious what's going to take the place of the $\omega$-REA operator and give you the needed inversion theorem. $\endgroup$
    – Peter Gerdes
    Commented Mar 23, 2023 at 4:53

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