Geodesic
Small Extensions of Models of $o$-Minimal Theories and Absolute Homogeneity
Matematičeskie trudy, Tome 10 (2007) no. 1, pp. 154-163.

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We obtain some results on existence of small extensions of models of weakly $o$-minimal atomic theories. In particular, we find a sharp upper estimate for the Hanf number of such a theory for omitting an arbitrary family of pure types. We also find a sharp upper estimate for cardinalities of weakly $o$-minimal absolutely homogeneous models and a sufficient condition for absolute homogeneity. 
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K. Zh. Kudaibergenov. Small Extensions of Models of $o$-Minimal Theories and Absolute Homogeneity. Matematičeskie trudy, Tome 10 (2007) no. 1, pp. 154-163. http://geodesic.mathdoc.fr/item/MT_2007_10_1_a6/

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