Categoricidad y amalgamación para clases elementales abstractas, y κ medible

In the original version of this paper, we assume a theory T in the logic Lκ,ℵ0 is categorical in a cardinal λ > κ, and κ is a measurable cardinal. There we prove that the class of models of T of cardinality < λ but ≥ |T| + κ has the amalgamation property under a natural order; this is a step toward understanding the character of such classes of models. In this revised version we replaced the class of models of T by k, an AEC (abstract elementary class) which has LST-number <κ, or at least which behaves nicely for ultra-powers by D, some normal ultra-filter on κ or just LST+k -complete non-principal ultra-filters on κ. Presently sub-section §2A deals with T ⊆ Lκ+,ℵ0 (and so does a large part of the introduction and little in the rest of §2), but otherwise, all is done in the context of AEC. The reader may in the first reading for transparency fix D, a normal ultrafilter on the measurable cardinal κ and either fix the T ⊆ Lκ,ℵ0 or fix an AEC k with LSTk < κ. We leave the original introduction adding a few comments at the end, after the three stars.