A strong failure of aleph_0-stability for atomic classes
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Publication:6282127
DOI10.1007/S00153-018-0623-6arXiv1701.05474MaRDI QIDQ6282127
Saharon Shelah, Michael C. Laskowski
Publication 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.
Classification theory, stability, and related concepts in model theory (03C45) Models with special properties (saturated, rigid, etc.) (03C50) Categoricity and completeness of theories (03C35)
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