Online research in philosophy

In this paper, we introduce a variety bdO of Ockham algebras with balanced double pseudocomplementation, consisting of those algebras of type where is an Ockham algebra, is a double p -algebra, and the operations and are linked by the identities [ f ( x )]* = [ f ( x )] + = f 2 ( x ), f ( x *) = x ** and f ( x + ) = x ++ . We give a description of the (...) congruences on the algebras, and show that there are precisely nine non-isomorphic subdirectly irreducible members in the class of the algebras via the Priestley duality. We also describe all axioms in the variety bdO , and provide a characterization of all subvarieties of bdO determined by 12 none-equivalent axioms, identifying therein the biggest subvariety in which every principal congruence is complemented. (shrink)

An algebra A is said to be congruence coherent if every subalgebra of A that contains a class of some congruence on A is a union of -classes. This property has been investigated in several varieties of lattice-based algebras. These include, for example, de Morgan algebras, p-algebras, double p-algebras, and double MS-algebras. Here we determine precisely when the property holds in the class of symmetric extended de Morgan algebras.