Abstract
A syntactic characterization is furnished for the class of elementary complete theories with finitely many countable models, which is the analog of a known theorem by Ryll-Nardzewski on countably categorical theories, and is based on classifying the theories by Rudin-Keisler quasiorders and distribution functions of a number of models limit over types.
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Sudoplatov, S.V. Complete Theories with Finitely Many Countable Models. I. Algebra and Logic 43, 62–69 (2004). https://doi.org/10.1023/B:ALLO.0000015131.41218.f4
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DOI: https://doi.org/10.1023/B:ALLO.0000015131.41218.f4