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)

@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}
}