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Descriptive Set Theory in the Category of Represented Spaces

Arno Pauly Orcid Logo, Matthew De Brecht

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science, Pages: 438 - 449

Swansea University Author: Arno Pauly Orcid Logo

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DOI (Published version): 10.1109/lics.2015.48

Abstract

We propose to extend descriptive set theory (DST)beyond its traditional setting of Polish spaces to the representedspaces. There, we can reformulate DST in terms of endofunctorson the categories of represented spaces and computable orcontinuous functions. In particular, this approach satisfies thede...

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Published in: 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
ISBN: 9781479988754
ISSN: 1043-6871
Published: IEEE 2015
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URI: https://cronfa.swan.ac.uk/Record/cronfa36020
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spelling 2021-01-28T13:03:35.3789106 v2 36020 2017-10-11 Descriptive Set Theory in the Category of Represented Spaces 17a56a78ec04e7fc47b7fe18394d7245 0000-0002-0173-3295 Arno Pauly Arno Pauly true false 2017-10-11 SCS We propose to extend descriptive set theory (DST)beyond its traditional setting of Polish spaces to the representedspaces. There, we can reformulate DST in terms of endofunctorson the categories of represented spaces and computable orcontinuous functions. In particular, this approach satisfies thedemand for a uniform approach to both classic and effectiveDST – computability follows naturally from the setting, ratherthan having to be explicitly demanded.The previous endeavour to extend DST to the Quasi-Polishspaces is subsumed by this work. In several cases the category-theoretic setting enables new, very succinct proofs; and sheds anew light on *why* certain results are true. The framework lets usmake formal some natural questions not easily approachable bytraditional methods. Conference Paper/Proceeding/Abstract 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science 438 449 IEEE 9781479988754 1043-6871 descriptive set theory, cartesian closed categories, computable analysis 1 7 2015 2015-07-01 10.1109/lics.2015.48 http://dx.doi.org/10.1109/lics.2015.48 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2021-01-28T13:03:35.3789106 2017-10-11T11:56:12.4650753 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Arno Pauly 0000-0002-0173-3295 1 Matthew De Brecht 2
title Descriptive Set Theory in the Category of Represented Spaces
spellingShingle Descriptive Set Theory in the Category of Represented Spaces
Arno Pauly
title_short Descriptive Set Theory in the Category of Represented Spaces
title_full Descriptive Set Theory in the Category of Represented Spaces
title_fullStr Descriptive Set Theory in the Category of Represented Spaces
title_full_unstemmed Descriptive Set Theory in the Category of Represented Spaces
title_sort Descriptive Set Theory in the Category of Represented Spaces
author_id_str_mv 17a56a78ec04e7fc47b7fe18394d7245
author_id_fullname_str_mv 17a56a78ec04e7fc47b7fe18394d7245_***_Arno Pauly
author Arno Pauly
author2 Arno Pauly
Matthew De Brecht
format Conference Paper/Proceeding/Abstract
container_title 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
container_start_page 438
publishDate 2015
institution Swansea University
isbn 9781479988754
issn 1043-6871
doi_str_mv 10.1109/lics.2015.48
publisher IEEE
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
url http://dx.doi.org/10.1109/lics.2015.48
document_store_str 0
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description We propose to extend descriptive set theory (DST)beyond its traditional setting of Polish spaces to the representedspaces. There, we can reformulate DST in terms of endofunctorson the categories of represented spaces and computable orcontinuous functions. In particular, this approach satisfies thedemand for a uniform approach to both classic and effectiveDST – computability follows naturally from the setting, ratherthan having to be explicitly demanded.The previous endeavour to extend DST to the Quasi-Polishspaces is subsumed by this work. In several cases the category-theoretic setting enables new, very succinct proofs; and sheds anew light on *why* certain results are true. The framework lets usmake formal some natural questions not easily approachable bytraditional methods.
published_date 2015-07-01T03:44:59Z
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score 11.013641

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