A Hierarchy of Immunity and Density for Sets of Reals

  • Takayuki Kihara
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)


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.


Open Ball Computable Function Computable Point Winning Strategy Learnable Function 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Takayuki Kihara
    • 1
  1. 1.Mathematical InstituteTohoku UniversitySendaiJapan

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