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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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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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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 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.
Item Description: Special issue from 6th Int. Conf. on Computability and Complexity in Analysis, Ljubljana, Slovenia
Keywords: stability of computability, realisability, domain representations
College: College of Science
Issue: 18
Start Page: 2496
End Page: 2522