We give an example of a countable theory T such that for every cardinal λ ≥ ℵ 2 there is a fully indiscernible set A of power λ such that the principal types are dense over A , yet there is no atomic model of T over A . In particular, T(A) is a theory of size λ where the principal types are dense, yet T(A) has no atomic model.
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Laskowski et al. (1993) studied this question.