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Conference on Computability in Europe

CiE 2012: How the World Computes pp 384–394Cite as

A Hierarchy of Immunity and Density for Sets of Reals

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7318))

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.

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Author information

Authors and Affiliations

  1. Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan

    Takayuki Kihara

Authors
  1. Takayuki Kihara
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Editors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. Computer Laboratory, University of Cambridge, Willialm Gates Building, J.J. Thomson Avenue, CB3 0FD, Cambridge, UK

    Anuj Dawar

  3. Institute for Logic, Language and Computation, University of Amsterdam, 1090 GE, Amsterdam, The Netherlands

    Benedikt Löwe

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© 2012 Springer-Verlag Berlin Heidelberg

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Kihara, T. (2012). A Hierarchy of Immunity and Density for Sets of Reals. In: Cooper, S.B., Dawar, A., Löwe, B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30870-3_39

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  • DOI: https://doi.org/10.1007/978-3-642-30870-3_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30869-7

  • Online ISBN: 978-3-642-30870-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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