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Checking Admissibility Using Natural Dualities

Checking Admissibility Using Natural Dualities This article presents a new method for obtaining small algebras to check the admissibility—equivalently, validity in free algebras—of quasi-identities in a finitely generated quasivariety. Unlike a previous algebraic approach of Metcalfe and Röthlisberger, which is feasible only when the relevant free algebra is not too large, this method exploits natural dualities for quasivarieties to work with structures of smaller cardinality and surjective rather than injective morphisms. A number of case studies are described here that could not be be solved using the algebraic approach, including (quasi)varieties of MS-algebras, double Stone algebras, and involutive Stone algebras. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2018 ACM
ISSN
1529-3785
eISSN
1557-945X
DOI
10.1145/3275115
Publisher site
See Article on Publisher Site

Abstract

This article presents a new method for obtaining small algebras to check the admissibility—equivalently, validity in free algebras—of quasi-identities in a finitely generated quasivariety. Unlike a previous algebraic approach of Metcalfe and Röthlisberger, which is feasible only when the relevant free algebra is not too large, this method exploits natural dualities for quasivarieties to work with structures of smaller cardinality and surjective rather than injective morphisms. A number of case studies are described here that could not be be solved using the algebraic approach, including (quasi)varieties of MS-algebras, double Stone algebras, and involutive Stone algebras.

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Dec 20, 2018

Keywords: Quasivariety

References