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arxiv: 1701.05474 · v1 · pith:KKYSVDUXnew · submitted 2017-01-19 · 🧮 math.LO

A strong failure of aleph₀-stability for atomic classes

classification 🧮 math.LO
keywords atomicaleph1classesmodelstherealephcompletecountable
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We study classes of atomic models At_T of a countable, complete first-order theory T . We prove that if At_T is not pcl-small, i.e., there is an atomic model N that realizes uncountably many types over pcl(a) for some finite tuple a from N, then there are 2^aleph1 non-isomorphic atomic models of T, each of size aleph1.

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