Subdirectly irreducible Ockham chains

We show that every subdirectly irreducible Ockham chain belongs to the generalised variety K-omega and is countable. Consideration of three particular types of finite Ockham chains, together with their order duals, leads to a determination of the structure of all finite subdirectly irreducible Ockham chains. These belong necessarily to the Berman classes K-1,K-q and we show that there are precisely 6(q) + 2 such chains in K-1,K-q. We also show that there are precisely 14 subdirectly irreducible Ockham chains whose endomorphism semigroup is regular, such chains having at most 5 elements.