CONSTRUCTING MANY ATOMIC MODELS IN ℵ1
John T. Baldwin, Michael Chris Laskowski, Saharon Shelah · Journal of Symbolic Logic · 2016
Abstract We introduce the notion of pseudoalgebraicity to study atomic models of first order theories (equivalently models of a complete sentence of ${L_{{\omega _1},\omega }}$ ). Theorem: Let T be any complete first-order theory in a countable language with an atomic model. If the pseudominimal types are not dense, then there are 2ℵ0 pairwise nonisomorphic atomic models of T, each of size ℵ1.