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arXiv · 1404.0297

Hyperprojective Hierarchy of QCB_0-spaces

Matthias Schröder·Victor Selivanov
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Abstract

We extend the Luzin hierarchy of qcb$_0$-spaces introduced in [ScS13] to all countable ordinals, obtaining in this way the hyperprojective hierarchy of qcb$_0$-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 qcb$_0$-spaces has much better closure properties than the category of projective qcb$_0$-space. As a result, there are natural examples of spaces that are hyperprojective but not projective.

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Matthias Schröder, Victor Selivanov. 2014-04-01. Hyperprojective Hierarchy of QCB_0-spaces. https://arxiv.org/abs/1404.0297

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