43 citations · 87 across the 9 of their papers we have counts for
12 papers
Coarse computability, the density metric, Hausdorff distances between Turing degrees, perfect trees, and reverse mathematics
Denis R. Hirschfeldt, Carl G. Jockusch, Paul E. Schupp
The coarse similarity class of is the set of all whose symmetric difference with has asymptotic density 0. There is a natural metric on the space $\mathcal{S}…
The reverse mathematics of Hindman's theorem for sums of exactly two elements
Barbara F. Csima, Damir D. Dzhafarov, Denis R. Hirschfeldt +3
Hindman's Theorem (HT) states that for every coloring of with finitely many colors, there is an infinite set such that all nonempty sums of dist…
Asymptotic Density and the Theory of Computability: A partial survey
Carl G. Jockusch, Paul E. Schupp
In this article we survey the development of generic and coarse computability and the main results on how classical asymptotic density interacts with the theory of computability.
Effectiveness of Hindman's theorem for bounded sums
Damir D. Dzhafarov, Carl G. Jockusch, Reed Solomon +1
We consider the strength and effective content of restricted versions of Hindman's Theorem in which the number of colors is specified and the length of the sums has a specified fin…
Asymptotic density and the coarse computability bound
Denis R. Hirschfeldt, Carl G. Jockusch, Timothy H. McNicholl +1
For we say that a set is \emph{coarsely computable at density} if there is a computable set such that has lower density…
Coarse Reducibility and Algorithmic Randomness
Denis R. Hirschfeldt, Carl G. Jockusch, Rutger Kuyper +1
A coarse description of a subset A of omega is a subset D of omega such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputabl…