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. 
@article{AL_2011_50_3_a1,
     author = {B. S. Baizhanov and V. V. Verbovskii},
     title = {$o$-stable theories},
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     pages = {303--325},
     publisher = {mathdoc},
     volume = {50},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2011_50_3_a1/}
}
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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/