Corrigendum à l'article "Sur la construction de certaines MS-algèbres" (Port. Math., 39(1-4) (1980), 489-496)
This paper gives a structure theorem for the class of countable 1-transitive coloured linear orderings for a countably infinite colour set, concluding the work begun in [1]. There we gave a complete classification of these orders for finite colour sets, of which there are ℵ₁. For infinite colour sets, the details are considerably more complicated, but many features from [1] occur here too, in more marked form, principally the use (now essential it seems) of coding trees, as a means of describing...
We construct a countable chain of Boolean semilattices, with all inclusion maps preserving the join and the bounds, whose union cannot be represented as the maximal semilattice quotient of the positive cone of any dimension group. We also construct a similar example with a countable chain of strongly distributive bounded semilattices. This solves a problem of F. Wehrung.