Canonical Effective Subalgebras of Classical Algebras as Constructive Metric Completions

Bauer, Andrej; Blanck, Jens

doi:10.4230/OASIcs.CCA.2009.2257

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Canonical Effective Subalgebras of Classical Algebras as Constructive Metric Completions

Authors Andrej Bauer, Jens Blanck

Part of: Volume: 6th International Conference on Computability and Complexity in Analysis (CCA'09) (CCA 2009)
Part of: Series: Open Access Series in Informatics (OASIcs)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2009-11-25

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DOI: 10.4230/OASIcs.CCA.2009.2257
URN: urn:nbn:de:0030-drops-22579

Subject Classification

Keywords

Effective algebras
realizability
constructive metric spaces

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/OASIcs.CCA.2009.2257

Author Details

Andrej Bauer

Jens Blanck

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