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.
M. de Brecht—Supported by JSPS Core-to-Core Program, A. Advanced Research Networks
M. Schröder—Supported by FWF research project “Definability and computability” and by DFG project Zi 1009/4-1.
V. Selivanov—Supported by the DFG Mercator professorship at the University of Würzburg, by the RFBR-FWF project “Definability and computability”, by RFBR project 13-01-00015a, and by 7th EU IRSES project 294962 (COMPUTAL).
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de Brecht, M., Schröder, M., Selivanov, V. (2015). Base-Complexity Classifications of QCB\(_0\)-Spaces. In: Beckmann, A., Mitrana, V., Soskova, M. (eds) Evolving Computability. CiE 2015. Lecture Notes in Computer Science(), vol 9136. Springer, Cham. https://doi.org/10.1007/978-3-319-20028-6_16
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DOI: https://doi.org/10.1007/978-3-319-20028-6_16
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