Priestley duality for MV-algebras and beyond

Author:

Fussner Wesley1,Gehrke Mai1,van Gool Samuel J.2ORCID,Marra Vincenzo3

Affiliation:

1. Laboratoire Mathématiques & Interactions J. A. Dieudonné , Université Côte d’Azur , Nice , France

2. IRIF , Université de Paris , Paris , France

3. Dipartimento di Matematica , Università degli Studi di Milano , Milano , Italy

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Natural dualities for varieties generated by finite positive MV-chains;Algebra universalis;2024-09-06

2. Semiconic idempotent logic I: Structure and local deduction theorems;Annals of Pure and Applied Logic;2024-07

3. Topological Duality and Algebraic Completions;Outstanding Contributions to Logic;2021-12-14

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