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Publication - Dr Charles Harris

    Avoiding uniformity in the δ2 0 enumeration degrees

    Citation

    Badillo, L & Harris, C, 2014, ‘Avoiding uniformity in the δ2 0 enumeration degrees’. Annals of Pure and Applied Logic, vol 165., pp. 1355-1379

    Abstract

    Defining a class of sets to be uniform  Δ20 if it is derived from a binary {0,1}{0,1}-valued function f≤TKf≤TK, we show that, for any C⊆DeC⊆De induced by such a class, there exists a high Δ20 degree c   which is incomparable with every degree b∈C∖{0e,0e′}.
    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 nonzero low degree caps with both a high and a nonzero low Δ20 degree.

    Full details in the University publications repository