The dual space of a doubleMS-algebra

Blyth, T. S.; Hansoul, Georges; Varlet, J. C.

doi:10.1007/bf01190408

Cited by 4 publications

(3 citation statements)

References 2 publications

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“…We have chosen in particular to study the variety of MSalgebras. This class of algebras was introduced by Blyth and Varlet as a common generalisation of De Morgan and Stone algebras; see [3]. This variety and the larger variety of Ockham algebras have been extensively studied in their own right.…”

Section: Case Studiesmentioning

confidence: 99%

Checking Admissibility Using Natural Dualities

Cabrer

Freisberg

Metcalfe

et al. 2018

ACM Trans. Comput. Logic

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This paper presents a new method for obtaining small algebras to check the admissibility-equivalently, validity in free algebras-of quasiidentities 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.

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Section: Case Studiesmentioning

confidence: 99%

Checking Admissibility Using Natural Dualities

Cabrer

Freisberg

Metcalfe

et al. 2018

ACM Trans. Comput. Logic

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show abstract

“…This duality for Ockham algebras restricts naturally to the five subvarieties from Figure 4: the descriptions of the dual spaces are summarised in Table 1 (see [8,10,4]…”

Section: Background: Ockham Algebrasmentioning

confidence: 99%

“…This duality for Ockham algebras restricts naturally to the five subvarieties from Figure 4: the descriptions of the dual spaces are summarised in Table 1 (see [8,10,4]). We finish this section by proving two basic facts about the duality for Ockham algebras that will be needed in later sections.…”

Section: Background: Ockham Algebrasmentioning

confidence: 99%