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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - E. A. Palyutin
TI  - Stably Definable Classes of Theories
JO  - Algebra i logika
PY  - 2005
SP  - 583
EP  - 600
VL  - 44
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2005_44_5_a3/
LA  - ru
ID  - AL_2005_44_5_a3
ER  - 
%0 Journal Article
%A E. A. Palyutin
%T Stably Definable Classes of Theories
%J Algebra i logika
%D 2005
%P 583-600
%V 44
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2005_44_5_a3/
%G ru
%F AL_2005_44_5_a3
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/

[1] S. Shelah, Classification theory and the number of non-isomorphic models, 2nd ed., Stud. Logic Found. Math., 92, North-Holland, Amsterdam a. o., 1990 | MR | Zbl

[2] L. van der Dries, Tame topology and $o$-minimal structures, Lond. Math. Soc. Lect. Note Ser., 248, Cambridge Univ. Press, Cambridge, 1998 | MR | Zbl

[3] E. A. Palyutin, “$E^*$-stabilnye teorii”, Algebra i logika, 42:2 (2003), 194–210 | MR | Zbl

[4] F. Wagner, Simple theories, Math. Appl. (Dordrecht), 503, Kluwer Academic Publishers, Dordrecht, 2000 | MR | Zbl

[5] Yu. L. Ershov, E. A. Palyutin, Matematicheskaya logika, Lan, Sankt-Peterburg–Moskva, 2004 | Zbl

[6] E. A. Palyutin, “Stabilno opredelimye klassy teorii”, Tezisy mezhd. konf. po algebre, logike i kibernetike, Irkutsk, 2004, 188