Hanf number of omitting type for simple first-order theories

Journal of Symbolic Logic 44 (3):319-324 (1979)
Let T be a complete countable first-order theory such that every ultrapower of a model of T is saturated. If T has a model omitting a type p in every cardinality $ then T has a model omitting p in every cardinality. There is also a related theorem, and an example showing the $\beth_\omega$ cannot be improved
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