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Canonical Effective Subalgebras of Classical Algebras as Constructive Metric Completions

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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.

BibTeX - Entry

@InProceedings{bauer_et_al:OASIcs:2009:2257,
  author =	{Andrej Bauer and Jens Blanck},
  title =	{{Canonical Effective Subalgebras of Classical Algebras as Constructive Metric Completions}},
  booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-12-5},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{11},
  editor =	{Andrej Bauer and Peter Hertling and Ker-I Ko},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2257},
  URN =		{urn:nbn:de:0030-drops-22579},
  doi =		{http://dx.doi.org/10.4230/OASIcs.CCA.2009.2257},
  annote =	{Keywords: Effective algebras, realizability, constructive metric spaces}
}

Keywords: Effective algebras, realizability, constructive metric spaces
Seminar: 6th International Conference on Computability and Complexity in Analysis (CCA'09)
Issue date: 2009
Date of publication: 2009


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