Under GCH, k(X) _< ~(X) for every homogeneous compactum X. CH implies that a homogeneous compactum of countable ~r-weight is first countable. There is a compact space of countable 7r-weight and uncountable character which is homogeneous under MA+-~CH, but not under CH.

In [4] Payne constructed such a pair of uncountable models for an uncountable language. Knight [1] announced that the language could be countable and presented her construction in [3] together with other examples one of which is a " nonSkolemizable elementary triple " of countable structures for a countable language. Payne's, Knight's and the present construction all seem to use rather differen...