A finite set of finite semilattices is said to be incomparably continuable if it can be extended to an infinite set of pairwise incomparable (with respect to embeddability) finite semilattices. After giving some simple examples we show that the set consisting of the four-element Boolean algebra and the four-element fork is incomparably continuable.
 R. McKenzie G. McNulty W. Taylor: Algebras, Lattices, Varieties, Vol. I
. Wadsworth & Brooks/Cole, Monterey, CA, 1987. MR 0883644