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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)

there is no one fundamental logical notion of necessity, nor consequently of possibility. If this conclusion is valid, the subject of modality ought to be banished from logic, since propositions are simply true or false. . .

A lambda theory satisfies an equation between contexts, where a context is a *-term with somè`holes'' in it, if all the instances of the equation fall within the lambda theory. In the main result of this paper it is shown that the equations (between contexts) valid in every lambda theory have an explicit finite equational axiomatization. The variety of… (More)