Coarse computability, the density metric, Hausdorff distances between Turing degrees, perfect trees, and reverse mathematics
The coarse similarity class $[A]$ of $A$ is the set of all $B$ whose symmetric difference with $A$ has asymptotic density 0. There is a natural metric $\delta$ on the space $\mathcal{S}$ of coarse similarity classes defined by letting $\delta([A],[B])$ be the upper density of the symmetric differenc...
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