Checking admissibility using natural dualities

Cabrer, Leonardo Manuel; Freisberg, Benjamin; Metcalfe, George; Priestley, Hilary (2019). Checking admissibility using natural dualities. ACM transactions on computational logic, 20(1), pp. 1-19. ACM

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This paper 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 that 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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Cabrer, Leonardo Manuel and Metcalfe, George

Subjects:

500 Science > 510 Mathematics

ISSN:

1529-3785

Publisher:

ACM

Language:

English

Submitter:

George Metcalfe

Date Deposited:

05 Feb 2019 13:23

Last Modified:

31 Oct 2019 09:22

ArXiv ID:

1801.02046v2

BORIS DOI:

10.7892/boris.123081

URI:

https://boris.unibe.ch/id/eprint/123081

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