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Canonical effective subalgebras of classical algebras as constructive metric completions

Andrej Bauer, Jens Blanck Orcid Logo

Journal of Universal Computer Science, Volume: 16, Issue: 18, Pages: 2496 - 2522

Swansea University Author: Jens Blanck Orcid Logo

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DOI (Published version): 10.3217/jucs-016-18-2496

Abstract

We prove general theorems about unique existence of effective subalgebras of classical algebras. The theorems are consequences of standard facts about completions of metric spaces within the framework of constructive mathematics, suitably interpreted in realizability models. We work with general rea...

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Published in: Journal of Universal Computer Science
ISSN: 0948-6968
Published: J.UCS Consortium 2010
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URI: https://cronfa.swan.ac.uk/Record/cronfa47
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spelling 2015-10-14T16:17:28.1703516 v2 47 2012-02-23 Canonical effective subalgebras of classical algebras as constructive metric completions 704f3ce6b65d931e1a86a03e9e30d639 0000-0001-9656-1352 Jens Blanck Jens Blanck true false 2012-02-23 SCS We prove general theorems about unique existence of effective subalgebras of classical algebras. The theorems are consequences of standard facts about completions of metric spaces within the framework of constructive mathematics, suitably interpreted in realizability models. We work with general realizability models rather than with a particular model of computation. Consequently, all the results are applicable in various established schools of computability, such as type 1 and type 2 effectivity, domain representations, equilogical spaces, and others. Journal Article Journal of Universal Computer Science 16 18 2496 2522 J.UCS Consortium 0948-6968 stability of computability, realisability, domain representations 28 9 2010 2010-09-28 10.3217/jucs-016-18-2496 Special issue from 6th Int. Conf. on Computability and Complexity in Analysis, Ljubljana, Slovenia COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2015-10-14T16:17:28.1703516 2012-02-23T17:01:54.0000000 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Andrej Bauer 1 Jens Blanck 0000-0001-9656-1352 2
title Canonical effective subalgebras of classical algebras as constructive metric completions
spellingShingle Canonical effective subalgebras of classical algebras as constructive metric completions
Jens Blanck
title_short Canonical effective subalgebras of classical algebras as constructive metric completions
title_full Canonical effective subalgebras of classical algebras as constructive metric completions
title_fullStr Canonical effective subalgebras of classical algebras as constructive metric completions
title_full_unstemmed Canonical effective subalgebras of classical algebras as constructive metric completions
title_sort Canonical effective subalgebras of classical algebras as constructive metric completions
author_id_str_mv 704f3ce6b65d931e1a86a03e9e30d639
author_id_fullname_str_mv 704f3ce6b65d931e1a86a03e9e30d639_***_Jens Blanck
author Jens Blanck
author2 Andrej Bauer
Jens Blanck
format Journal article
container_title Journal of Universal Computer Science
container_volume 16
container_issue 18
container_start_page 2496
publishDate 2010
institution Swansea University
issn 0948-6968
doi_str_mv 10.3217/jucs-016-18-2496
publisher J.UCS Consortium
college_str Faculty of Science and Engineering
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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
document_store_str 0
active_str 0
description We prove general theorems about unique existence of effective subalgebras of classical algebras. The theorems are consequences of standard facts about completions of metric spaces within the framework of constructive mathematics, suitably interpreted in realizability models. We work with general realizability models rather than with a particular model of computation. Consequently, all the results are applicable in various established schools of computability, such as type 1 and type 2 effectivity, domain representations, equilogical spaces, and others.
published_date 2010-09-28T03:03:10Z
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score 10.952064

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