The Dual Space Of Balanced Pseudocomplemented Ockham Algebras

In this thesis, we are mostly concerned with the dual space of a balancedpseudocomplemented Ockham algebra, namely bpO-space. We say that analgebra (L;∧,∨,* ,f,0,1) is a balanced pseudocomplemented Ockham algebra(shortly, bpO-algebra) if (L;∧,∨,* ,0,1) is a distributive pseudocomplementedalgebra with a dual endomorphism f such that f(x^*) = x^** and [f(x)]^* = f²(x)for every x∈L.The main results in this thesis are to extend Priestley's duality and Urquhart'stheorem to the variety of bpO and show that there are exactly 15 non-equivalentaxioms in bpO-space, these axioms can be translated into inequalities in thevariety of bpO as follows:We also provide a characterization of all subvarieties of the variety of bpO bymeans of the axioms.Finally, we apply the characterization theorem to the construction of dis-tributive lattices on which there can be defined (up to isomorphism) a uniquebpO which belongs to a preassigned class.