Geodesic
Linearly Ordered Theories which are Nearly Countably Categorical
Matematičeskie zametki, Tome 101 (2017) no. 3, pp. 413-424

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The notions of almost $\omega$-categoricity and 1-local $\omega$-categoricity are studied. In particular, necessary and sufficient conditions for their equivalence under additional assumptions are found. It is proved that 1-local $\omega$-categorical theories on dense linear orders are Ehrenfeucht and that Ehrenfeucht quite o-minimal binary theories are almost $\omega$-categorical.
Keywords: linear order, almost $\omega$-categoricity, $1$-local $\omega$-categoricity, Ehrenfeucht theory, weak o-minimality, quite o-minimality, binary theory, convexity rank. 
@article{MZM_2017_101_3_a7,
     author = {B. Sh. Kulpeshov and S. V. Sudoplatov},
     title = {Linearly {Ordered} {Theories} which are {Nearly} {Countably} {Categorical}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {413--424},
     publisher = {mathdoc},
     volume = {101},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_3_a7/}
}
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B. Sh. Kulpeshov; S. V. Sudoplatov. Linearly Ordered Theories which are Nearly Countably Categorical. Matematičeskie zametki, Tome 101 (2017) no. 3, pp. 413-424. http://geodesic.mathdoc.fr/item/MZM_2017_101_3_a7/