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Stability of representations of effective partial algebrasPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2011 (English)In: Mathematical logic quarterly, ISSN 0942-5616, E-ISSN 1521-3870, Vol. 57, no 2, 217-231 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2011. Vol. 57, no 2, 217-231 p.
##### Keyword [en]

Numberings, recursive equivalence, computable stability, effective partial algebras, computable real numbers, ultrametric algebras, metric algebras
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-152783DOI: 10.1002/malq.200910133ISI: 000289005900009OAI: oai:DiVA.org:uu-152783DiVA: diva2:414077
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Available from: 2011-05-02 Created: 2011-05-02 Last updated: 2012-02-16Bibliographically approved

An algebra is effective if its operations are computable under some numbering. When are two numberings of an effective partial algebra equivalent? For example, the computable real numbers form an effective field and two effective numberings of the field of computable reals are equivalent if the limit operator is assumed to be computable in the numberings (theorems of Moschovakis and Hertling). To answer the question for effective algebras in general, we give a general method based on an algebraic analysis of approximations by elements of a finitely generated subalgebra. Commonly, the computable elements of a topological partial algebra are derived from such a finitely generated algebra and form a countable effective partial algebra. We apply the general results about partial algebras to the recursive reals, ultrametric algebras constructed by inverse limits, and to metric algebras in general.

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