The dual space of a finite simple Ockham algebra

Abstract

Abstract We recall that an n-crown (with n; ≥2) is an ordered set C with 2n elements x 1, ... , x2n whose only comparabilities are An n-crown C is connected, has length 1, |Max 𝒞|𝒞; = |Min 𝒞|= n, every minimal element is covered by two maximal elements, and every maximal element covers two minimal elements; so all vertices of 𝒞 have degree 2. There have been some attempts to generalise this notion. We mention two of these. In [93], W. T. Trotter, Jr. defines a crown Snk as follows : for n ≥ 3 and k ≥ :0, Snk is an ordered set of length 1 with n +; k minimal elements a1, ... , an+k and n + k maximal elements b1, ... , bn+k each a;I being incomparable with bi, ... , bi;+k and being covered by the remaining n - l maximal elements. Here, of course, the subscripts have to be interpreted cyclically. For example, the graph of S42 is as follows :