Contributions to the theory of Ockham algebras

In the first part of this thesis we consider particular ordered sets (connected and of small height) and determine the cardinality of the corresponding dual MS - algebra and of its set of fixed points. The remainder of the thesis is devoted to a study of congruences of Ockham algebras and a generalised variety K of Ockham algebras that contains all of the Berman varieties K[sub]p,[sub]q. In particular we consider the congruences [sub]i(i = 1, 2,...) defined on an Ockham algebra (L; f) by (x, y) ∊ [sub]i ⇔ fⁱ(x)= fⁱ(y) and show that (L; f) ∊ K is subdirectly irreducible if and only if the lattice of congruences of L reduces to the chain = ₀ ≤ ₁≤ ₂≤ … ≤< Where = ⌵ [sub]i≥0i. Finally we obtain a characterisation of the finite simple Ockham algebras