Hyperprojective Hierarchy of qcb0-Spaces

  • Matthias Schröder
  • Victor Selivanov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8493)

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.

Keywords

Hyperprojective hierarchy qcb0-space continuous functionals of countable types cartesian closed category 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Matthias Schröder
    • 1
  • Victor Selivanov
    • 2
  1. 1.Kurt Gödel Research Center, University of ViennaAustria
  2. 2.A.P. Ershov Institute of Informatics Systems SB RASNovosibirskRussia

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