On the existence of atomic models

Abstract

AbstractWe give an example of a countable theory T such that for every cardinal λ ≥ ℵ2 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.