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Hyperprojective hierarchy of qcb0-spaces. / Schröder, Matthias; Selivanov, Victor.

In: Computability, Vol. 4, No. 1, 01.01.2015, p. 1-17.

Research output: Contribution to journal › Article › peer-review

Harvard

Schröder, M & Selivanov, V 2015, 'Hyperprojective hierarchy of qcb0-spaces', Computability, vol. 4, no. 1, pp. 1-17. https://doi.org/10.3233/COM-150031

APA

Schröder, M., & Selivanov, V. (2015). Hyperprojective hierarchy of qcb0-spaces. Computability, 4(1), 1-17. https://doi.org/10.3233/COM-150031

Vancouver

Schröder M, Selivanov V. Hyperprojective hierarchy of qcb0-spaces. Computability. 2015 Jan 1;4(1):1-17. https://doi.org/10.3233/COM-150031

Author

Schröder, Matthias ; Selivanov, Victor. / Hyperprojective hierarchy of qcb0-spaces. In: Computability. 2015 ; Vol. 4, No. 1. pp. 1-17.

BibTeX

@article{8827711d3a574745b3758f1c342e5931,
title = "Hyperprojective hierarchy of qcb0-spaces",
abstract = "We extend the recently introduced Luzin hierarchy of qcb0-spaces to all countable ordinals, obtaining in this way the hyperprojective hierarchy of qcb0-spaces. We generalize all main results for the former hierarchy 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-spaces. As a result, there are natural examples of spaces that are hyperprojective but not projective.",
keywords = "Cartesian closed category, continuous functionals of countable types, Hyperprojective hierarchy, qcb0-space",
author = "Matthias Schr{\"o}der and Victor Selivanov",
year = "2015",
month = jan,
day = "1",
doi = "10.3233/COM-150031",
language = "English",
volume = "4",
pages = "1--17",
journal = "Computability",
issn = "2211-3568",
publisher = "IOS Press",
number = "1",

}

RIS

TY - JOUR

T1 - Hyperprojective hierarchy of qcb0-spaces

AU - Schröder, Matthias

AU - Selivanov, Victor

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We extend the recently introduced Luzin hierarchy of qcb0-spaces to all countable ordinals, obtaining in this way the hyperprojective hierarchy of qcb0-spaces. We generalize all main results for the former hierarchy 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-spaces. As a result, there are natural examples of spaces that are hyperprojective but not projective.

AB - We extend the recently introduced Luzin hierarchy of qcb0-spaces to all countable ordinals, obtaining in this way the hyperprojective hierarchy of qcb0-spaces. We generalize all main results for the former hierarchy 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-spaces. As a result, there are natural examples of spaces that are hyperprojective but not projective.

KW - Cartesian closed category

KW - continuous functionals of countable types

KW - Hyperprojective hierarchy

KW - qcb0-space

UR - http://www.scopus.com/inward/record.url?scp=85011083071&partnerID=8YFLogxK

U2 - 10.3233/COM-150031

DO - 10.3233/COM-150031

M3 - Article

AN - SCOPUS:85011083071

VL - 4

SP - 1

EP - 17

JO - Computability

JF - Computability

SN - 2211-3568

IS - 1

ER -

ID: 126986033