We study when classes can have the disjoint amalgamation property for a proper initial segment of cardinals. For every natural number k, there is a class K k , defined by a sentence in L ω1,ω that has no models of cardinality greater than ℶ k + 1, but K k has the disjoint amalgamation property on models of cardinality less than or equal to ℵ k − 3 and has models of cardinality ℵ k − 1. More strongly, we can have disjoint amalgamation up to ℵ ∝ for ∝ < ω 1, but have a bound on size of models.

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... For every countable ordinal ∝, there is a class K ∝ defined by a sentence in L ω1,ω that has no models of cardinality greater than ℶω1, but K does have the disjoint amalgamation property on models of cardinality less than or equal to ℵ∝ . Finally we show that we can extend the ℵ∝ to ℶ ∝ in the second theorem consistently with ZFC and while having ℵ i ≪ ℶ i for 0 < i < ∝. Similar results hold for arbitrary ordinals ∝ with ∣∝∣ = k and Lk + ω .