Subdirectly Irreducibility And Axioms In The Relative Ockham Algebras

In this thesis we firstly study a particular subclass of pseudocomplemented Ockham algebras (L;∧,∨, f,^*, 0, 1) where (L;∧,∨, f, 0, 1) is an Ockham algebra, (L;∧,∨,^*, 0, 1) is a p-algebra, and the operations x(?)f(x) and x(?)x^* satisfy the identities f(x^*) = x^** and [f(x)]^* = f²(x). We shall denote by bpO the class of these algebras. We show that if L∈bpO is subdirectly irreducible then Con L is a chain of the form:. Furthermore, we show that there are precisely eleven non-isomorphic subdirectly irreducible members in the class of these algebras and give a complete description of them.We also investigate the axioms in the variety eO of extended Ockham algebras. We extend Urquhart's theorem to eO-algebras and we are in particular concerned with the subclass e₂M of eO-algebras in which f² = id and k² = id. We show that there are 19 non-equivalent axioms in e₂M and then order them by implication.