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Hyperprojective Hierarchy of qcb0-Spaces

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Language, Life, Limits (CiE 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8493))

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Abstract

We extend the Luzin hierarchy of qcb0-spaces introduced in [ScS13] to all countable ordinals, obtaining in this way the hyperprojective hierarchy of qcb0-spaces. We generalize all main results of [ScS13] to this larger hierarchy. In particular, we extend the Kleene-Kreisel continuous functionals of finite types to the continuous functionals of countable types and relate them to the new hierarchy. We show that the category of hyperprojective qcb0-spaces has much better closure properties than the category of projective qcb0-space. As a result, there are natural examples of spaces that are hyperprojective but not projective.

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Author information

Authors and Affiliations

  1. Kurt Gödel Research Center, University of Vienna, Austria

    Matthias Schröder

  2. A.P. Ershov Institute of Informatics Systems SB RAS, Novosibirsk, Russia

    Victor Selivanov

Authors
  1. Matthias Schröder
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  2. Victor Selivanov
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Editor information

Editors and Affiliations

  1. College of Science, Department of Computer Science, Swansea University, SA2 8PP, Swansea, UK

    Arnold Beckmann

  2. Department of Algorithms and Their Applications, Eötvös Loránd University, Pázmány Péter sétány 1/c,, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  3. Computer Science Institute, Brandenburg University of Technology Cottbus-Senftenberg, Cottbus, Germany

    Klaus Meer

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Schröder, M., Selivanov, V. (2014). Hyperprojective Hierarchy of qcb0-Spaces. In: Beckmann, A., Csuhaj-Varjú, E., Meer, K. (eds) Language, Life, Limits. CiE 2014. Lecture Notes in Computer Science, vol 8493. Springer, Cham. https://doi.org/10.1007/978-3-319-08019-2_37

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  • DOI: https://doi.org/10.1007/978-3-319-08019-2_37

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08018-5

  • Online ISBN: 978-3-319-08019-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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