Avoiding uniformity in theΔ20enumeration degrees

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Avoiding uniformity in the Δ20 enumeration degrees

Defining a class of sets to be uniform ∆2 if it is derived from a binary {0, 1}-valued function f≤TK, we show that, for any C ⊆ De induced by such a class, there exists a high ∆2 degree c which is incomparable with every degree b ∈ C \ {0e,0′e }. We show how this result can be applied to quite general subclasses of the Ershov Hierarchy and we also prove, as a direct corollary, that every nonzer...

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ژورنال

عنوان ژورنال: Annals of Pure and Applied Logic

سال: 2014

ISSN: 0168-0072

DOI: 10.1016/j.apal.2014.04.008