Submission date: 19 January 2017

Abstract:

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.

Mathematics Subject Classification: 03C45, 03C75

Keywords and phrases:

Full text arXiv 1701.05474: pdf, ps.