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    Constructing many atomic models in ℵ1

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    Date
    2016-09
    Author
    Baldwin, JT
    Laskowski, MC
    Shelah, S
    Publisher
    Association for Symbolic Logic
    Metadata
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    Abstract
    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.
    Type
    Article
    Date available in INDIGO
    2016-12-19T16:35:40Z
    URI
    http://hdl.handle.net/10027/21429
    Collections
    • Publications - Mathematics, Statistics, and Computer Science

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