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On the existence of atomic models

Michael C. Laskowski·Saharon Shelah
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Abstract

We give an example of a countable theory T such that for every cardinal lambda >= aleph_2 there is a fully indiscernible set A of power lambda 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 lambda where the principal types are dense, yet T(A) has no atomic model.

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Michael C. Laskowski, Saharon Shelah. 1993-01-15. On the existence of atomic models. https://arxiv.org/abs/math/9301210

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