Canonical Effective Subalgebras of Classical Algebras as Constructive Metric Completions

Authors Andrej Bauer, Jens Blanck

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Andrej Bauer
Jens Blanck

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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)


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.
  • Effective algebras
  • realizability
  • constructive metric spaces


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