Constructing many atomic models in ℵ1
PublisherAssociation for Symbolic Logic
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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.