Geodesic
Stably Definable Classes of Theories
Algebra i logika, Tome 44 (2005) no. 5, pp. 583-600

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A question is studied as to which properties (classes) of elementary theories can be defined via generalized stability. We present a topological account of such classes. It is stated that some well-known classes of theories, such as strongly minimal, $o$-minimal, simple, etc., are stably definable, whereas, for instance, countably categorical, almost strongly minimal, $\omega$-stable ones, are not.
Keywords: elementary theory, stably definable class. 
@article{AL_2005_44_5_a3,
     author = {E. A. Palyutin},
     title = {Stably {Definable} {Classes} of {Theories}},
     journal = {Algebra i logika},
     pages = {583--600},
     publisher = {mathdoc},
     volume = {44},
     number = {5},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2005_44_5_a3/}
}
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E. A. Palyutin. Stably Definable Classes of Theories. Algebra i logika, Tome 44 (2005) no. 5, pp. 583-600. http://geodesic.mathdoc.fr/item/AL_2005_44_5_a3/