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Priestley duality for MV-algebras and beyond

Wesley Fussner, Mai Gehrke, Samuel J. van Gool ORCID logo and Vincenzo Marra
From the journal Forum Mathematicum

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.

MSC 2010: 06D50; 06D35; 03G10

  1. Communicated by: Manfred Droste

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Received: 2020-05-08
Revised: 2020-10-20
Published Online: 2021-05-12
Published in Print: 2021-07-01

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