journal contribution posted on 19.12.2016, 00:00 by JT Baldwin, MC Laskowski, S Shelah
We introduce the notion of pseudo-algebraicity to study atomic models of first
order theories (equivalently models of a complete sentence of Lω1,ω). Theorem: Let
T be any complete first-order theory in a countable language with an atomic model. If
the pseudo-minimal types are not dense, then there are 2
ℵ1 pairwise non-isomorphic
atomic models of T, each of size ℵ1.
Research partially supported by Simons travel grant G5402 Partially supported by NSF grant DMS-1308546.This research was partially supported by NSF grant DMS 1101597. The third author was partially supported by the European Research Council grant 338821.
Publisher StatementThis is a non-final version of an article published in final form in: Baldwin, J. T., Laskowski, M. C. and Shelah, S. CONSTRUCTING MANY ATOMIC MODELS IN N-1. Journal of Symbolic Logic. 2016. 81(3): 1142-1162. DOI: 10.1017/jsl.2015.81.
PublisherAssociation for Symbolic Logic