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A variety V of Boolean algebras with operators is singleton-persistent if it contains a complex algebra whenever it contains the subalgebra generated by the singletons. V is atom-canonical if it contains the complex algebra of the atom structure of any of the atomic members of V. This paper explores relationships between these " persistence " properties and(More)
1 abstract. A structural semantics is developed for a first-order logic, with infinite disjunctions and conjunctions, that is characterised algebraically by quantales. The model structures involved combine the " covering systems " approach of Kripke-Joyal intuitionistic semantics from topos theory with the ordered groupoid structures used to model various(More)