Priestley duality for MV-algebras and beyond
Logic
2023-07-24 v4
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.
Cite
@article{arxiv.2002.12715,
title = {Priestley duality for MV-algebras and beyond},
author = {Wesley Fussner and Mai Gehrke and Sam van Gool and Vincenzo Marra},
journal= {arXiv preprint arXiv:2002.12715},
year = {2023}
}