On Density of Pairs of Natural Numbers
Rzepecka, Genowefa (2015-12-08T07:20:54Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Rzepecka, Genowefa (2015-12-08T07:20:54Z)
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In this paper it is discus a relation between -density and -density. A generalization of Šalát’s result concerning this relation in the case of asymptotic density is proved.
Michał Lorens (1974)
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Let r ∈ [0,1]. A set A ⊆ ω is said to be coarsely computable at density r if there is a computable function f such that {n | f(n) = A(n)} has lower density at least r. Our main results are that A is coarsely computable at density 1/2 if A is computably traceable or truth-table reducible to a 1-random set. In the other direction, we show that if a degree a is hyperimmune or PA, then there is an a-computable set which is not coarsely computable at any positive density.