Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Computable analysis: an introduction
Computable analysis: an introduction
Computability on subsets of metric spaces
Theoretical Computer Science - Topology in computer science
Topological aspects of the Medvedev lattice
Archive for Mathematical Logic
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The notion of immunity is useful to classify degrees of noncomputability. Meanwhile, the notion of immunity for topological spaces can be thought of as an opposite notion of density. Based on this viewpoint, we introduce a new degree-theoretic invariant called layer density which assigns a value n to each subset of Cantor space. Armed with this invariant, we shed light on an interaction between a hierarchy of density/immunity and a mechanism of type-two computability.