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Canonical Effective Subalgebras of Classical Algebras as Constructive Metric Completions Bauer, Andrej Blanck, Jens Effective algebras realizability constructive metric spaces 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Andrej Bauer and Jens Blanck 2009 Is Part Of OASIcs, Volume 11, 6th International Conference on Computability and Complexity in Analysis (CCA'09) (2009) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/OASIcs.CCA.2009.2257 urn:nbn:de:0030-drops-22579 https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2257 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode