A strong failure of aleph_0-stability for atomic classes
Logic
2017-01-20 v1
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.
Keywords
Cite
@article{arxiv.1701.05474,
title = {A strong failure of aleph_0-stability for atomic classes},
author = {Michael C. Laskowski and Saharon Shelah},
journal= {arXiv preprint arXiv:1701.05474},
year = {2017}
}