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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Base-Complexity Classifications of QCB\(_0\)-Spaces
verfasst von : Matthew de Brecht, Matthias Schröder, Victor Selivanov
Erschienen in: Evolving Computability
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Abstract
We define and study new classifications of qcb\(_0\)-spaces based on the idea to measure the complexity of their bases. The new classifications complement those given by the hierarchies of qcb\(_0\)-spaces introduced in [7, 8] and provide new tools to investigate non-countably based qcb\(_0\)-spaces. As a by-product, we show that there is no universal qcb\(_0\)-space and establish several apparently new properties of the Kleene-Kreisel continuous functionals of countable types.