Geodesic
$o$-stable theories
Algebra i logika, Tome 50 (2011) no. 3, pp. 303-325.

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A well-developed technique created to study stable theories (M. Morley, S. Shelah) is applied in dealing with a class of theories with definable linear order. We introduce the notion of an $o$-stable theory, which generalizes the concepts of $o$-minimality, of weak $o$-minimality, and of quasi-$o$-minimality. It is proved that $o$-stable theories are dependent, but they do not exhaust the class of dependent theories with definable linear order, and that every linear order is $o$-superstable.
Keywords: $o$-stable theory, dependent theory, convex complete 1-type. 
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B. S. Baizhanov; V. V. Verbovskii. $o$-stable theories. Algebra i logika, Tome 50 (2011) no. 3, pp. 303-325. http://geodesic.mathdoc.fr/item/AL_2011_50_3_a1/

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