Ockham algebras with balanced double pseudocomplementation

Studia Logica 90 (2):189 - 209 (2008)
Abstract
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.
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