Submission date: 1 March 2015.

Abstract:

We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of L_{ω_1,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^{ℵ_1} pairwise non-isomorphic atomic models of T, each of size ℵ_1.

Mathematics Subject Classification: 03C350, 03C375

Keywords and phrases:

Full text arXiv 1503.00318: pdf, ps.