# Sh:1099

- Laskowski, M. C., & Shelah, S. (2019).
*A strong failure of \aleph_0-stability for atomic classes*. Arch. Math. Logic,**58**(1-2), 99–118. arXiv: 1701.05474 DOI: 10.1007/s00153-018-0623-6 MR: 3902807 -
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 aleph_1. - published version (20p)

Bib entry

@article{Sh:1099, author = {Laskowski, Michael Chris and Shelah, Saharon}, title = {{A strong failure of $\aleph_0$-stability for atomic classes}}, journal = {Arch. Math. Logic}, fjournal = {Archive for Mathematical Logic}, volume = {58}, number = {1-2}, year = {2019}, pages = {99--118}, issn = {0933-5846}, mrnumber = {3902807}, mrclass = {03C50 (03C35)}, doi = {10.1007/s00153-018-0623-6}, note = {\href{https://arxiv.org/abs/1701.05474}{arXiv: 1701.05474}}, arxiv_number = {1701.05474} }