Many thanks to the people who pointed me in the direction of the literature on free Heyting semilattices. With its help, I have now managed to answer the question that led me to think about them in the first place: There are exactly 489 different Mal'cev operations in the theory of Heyting semilattices. (There are infinitely many in Heyting algebras, and I had idly wondered whether the same might be true if you leave out disjunction.) Note that 489 = 3 x 163: this is not a coincidence, though why Eddington's favourite prime appears in this context I don't know. Rather to my surprise, there is only one Pixley operation (that is, a Mal'cev operation p satisfying the additional equation p(x,y,x) = y). There are many different ways of describing it, but they all turn out to be equal as members of the free Heyting semilattice HS(3). Peter Johnstone 20-Jan-2005 15:07:43 -0400,2069;000000000000-00000000