Abstract
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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Original Russian Text © K. Zh. Kudaibergenov, 2007, published in Matematicheskie Trudy, 2007, Vol. 10, No. 1, pp. 154–163.
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Kudaibergenov, K.Z. Small extensions of models of o-minimal theories and absolute homogeneity. Sib. Adv. Math. 18, 118–123 (2008). https://doi.org/10.3103/S1055134408020053
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DOI: https://doi.org/10.3103/S1055134408020053