Geodesic
Finding $2^{\aleph_0}$ countable models for ordered theories
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 719-727

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The article is focused on finding conditions that imply small theories of linear order have the maximum number of countable non-isomorphic models. We introduce the notion of extreme triviality of non-principal types, and prove that a theory of order, which has such a type, has $2^{\aleph_0}$ countable non-isomorphic models.
Keywords: countable model, linear order, omitting types. 
@article{SEMR_2018_15_a19,
     author = {B. Baizhanov and J. T. Baldwin and T. Zambarnaya},
     title = {Finding $2^{\aleph_0}$ countable models for ordered theories},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {719--727},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a19/}
}
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B. Baizhanov; J. T. Baldwin; T. Zambarnaya. Finding $2^{\aleph_0}$ countable models for ordered theories. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 719-727. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a19/