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CONSTRUCTING MANY ATOMIC MODELS IN ℵ1
Published online by Cambridge University Press: 14 September 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.
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- Copyright © The Association for Symbolic Logic 2016
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