We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions.

Priestley duality for MV-algebras and beyond / W. Fussner, M. Gehrke, S.J. Van Gool, V. Marra. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - 33:4(2021 Jul 01), pp. 899-921. [10.1515/forum-2020-0115]

Priestley duality for MV-algebras and beyond

V. Marra
2021

Abstract

We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions.
canonical extensions; monoidal t-norm logic; MV-algebras; partial topological algebra; Priestley duality
Settore MAT/01 - Logica Matematica
Settore MAT/02 - Algebra
12-mag-2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/865045
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