Journal of Symbolic Logic 63 (3):891-896 (1998)

Abstract
Strengthening a theorem of D.W. Kueker, this paper completely characterizes which countable structures do not admit uncountable L ω 1 ω -elementarily equivalent models. In particular, it is shown that if the automorphism group of a countable structure M is abelian, or even just solvable, then there is no uncountable model of the Scott sentence of M. These results arise as part of a study of Polish groups with compatible left-invariant complete metrics
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DOI 10.2307/2586718
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The Vaught Conjecture: Do Uncountable Models Count?John T. Baldwin - 2007 - Notre Dame Journal of Formal Logic 48 (1):79-92.

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