Abstract
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. © 2012 Springer-Verlag.
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CITATION STYLE
Kihara, T. (2012). A hierarchy of immunity and density for sets of reals. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7318 LNCS, pp. 384–394). https://doi.org/10.1007/978-3-642-30870-3_39
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