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# The Dual Space of a Finite Simple Ockham Algebra

T. S. Blyth and J. C. Varlet
Studia Logica: An International Journal for Symbolic Logic
Vol. 56, No. 1/2, Priestley Duality (Jan. - Mar., 1996), pp. 3-21
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015835
Page Count: 19
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## Abstract

Let (L; f) be a finite simple Ockham algebra and let (X; g) be its dual space. We first prove that every connected component of X is either a singleton or a generalised crown (i.e. an ordered set that is connected, has length 1, and all vertices of which have the same degree). The representation of a generalised crown by a square (0, 1)-matrix in which all line sums are equal is used throughout, and a complete description of X, including the number of connected components and the degree of the vertices, is given. We then examine the converse problem of when a generalised crown can be made into a connected component of (X; g). We also determine the number of non-isomorphic finite simple Ockham algebras that belong properly to a given subvariety $\text{P}_{2n,0}$. Finally, we show that the number of fixed points of (L; f) is 0, 1, or 2 according to the nature of X.

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