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DOI: 10.4230/OASIcs.CCA.2009.2257

Canonical Effective Subalgebras of Classical Algebras as Constructive Metric Completions

Authors: Andrej Bauer and Jens Blanck

Published in: OASIcs, Volume 11, 6th International Conference on Computability and Complexity in Analysis (CCA'09) (2009)

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.

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Andrej Bauer and Jens Blanck. Canonical Effective Subalgebras of Classical Algebras as Constructive Metric Completions. In 6th International Conference on Computability and Complexity in Analysis (CCA'09). Open Access Series in Informatics (OASIcs), Volume 11, pp. 37-48, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{bauer_et_al:OASIcs.CCA.2009.2257,
  author =	{Bauer, Andrej and Blanck, Jens},
  title =	{{Canonical Effective Subalgebras of Classical Algebras as Constructive Metric Completions}},
  booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
  pages =	{37--48},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-12-5},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{11},
  editor =	{Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2257},
  URN =		{urn:nbn:de:0030-drops-22579},
  doi =		{10.4230/OASIcs.CCA.2009.2257},
  annote =	{Keywords: Effective algebras, realizability, constructive metric spaces}
}

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Canonical Effective Subalgebras of Classical Algebras as Constructive Metric Completions

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