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We study the degree spectra and reverse-mathematical applications of computably enumerable and co-computably enu-merable partial orders. We formulate versions of the chain/antichain principle and ascending/descending sequence principle for such orders , and show that the latter is strictly stronger than the latter. We then show that every ∅-computable… (More)

In this paper, we investigate connections between structures present in every generic extension of the universe V and computability theory. We introduce the notion of generic Muchnik reducibility that can be used to to compare the complexity of uncountable structures; we establish basic properties of this reducibility, and study it in the context of generic… (More)

We study a class of operators on Turing degrees arising naturally from ultrafilters. Suppose U is a nonprincipal ultrafilter on ω. We can then view a sequence of sets A = (Ai)i∈ω as an " approximation " of a set B produced by taking the limits of the Ai via U: we set limU (A) = {x : {i : x ∈ Ai} ∈ U}. This can be extended to the Turing degrees, by defining… (More)

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