Geodesic
Preservation and violation of homogeneity of models under a~special expansion
Matematičeskie trudy, Tome 12 (2009) no. 1, pp. 117-129.

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

Conditions are found under which homogeneity of a model $M$ implies homogeneity of the model $M^\mathrm{eq}$. One of these conditions is $\omega$-stability of the theory of $M$. Examples are constructed of superstable theories for which homogeneity is not preserved under such a passage. 
@article{MT_2009_12_1_a3,
     author = {K. Zh. Kudaibergenov},
     title = {Preservation and violation of homogeneity of models under a~special expansion},
     journal = {Matemati\v{c}eskie trudy},
     pages = {117--129},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2009_12_1_a3/}
}
TY  - JOUR
AU  - K. Zh. Kudaibergenov
TI  - Preservation and violation of homogeneity of models under a~special expansion
JO  - Matematičeskie trudy
PY  - 2009
SP  - 117
EP  - 129
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2009_12_1_a3/
LA  - ru
ID  - MT_2009_12_1_a3
ER  - 
%0 Journal Article
%A K. Zh. Kudaibergenov
%T Preservation and violation of homogeneity of models under a~special expansion
%J Matematičeskie trudy
%D 2009
%P 117-129
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2009_12_1_a3/
%G ru
%F MT_2009_12_1_a3
K. Zh. Kudaibergenov. Preservation and violation of homogeneity of models under a~special expansion. Matematičeskie trudy, Tome 12 (2009) no. 1, pp. 117-129. http://geodesic.mathdoc.fr/item/MT_2009_12_1_a3/

[1] Kudaibergenov K. Zh., “Ob odnorodnykh modelyakh odnorazmernostnykh teorii”, Algebra i logika, 34:1 (1995), 61–78 | MR | Zbl

[2] Kudaibergenov K. Zh., “Odnorodnye modeli i stabilnye diagrammy”, Sib. mat. zhurn., 43:5 (2002), 1064–1076 | MR | Zbl

[3] Buechler S., Lessmann O., “Simple homogeneous models”, J. Amer. Math. Soc. (electronic), 16:1 (2002), 91–121 | DOI | MR

[4] Keisler H. J., Morley M. D., “On the number of homogeneous models of a given power”, Israel J. Math., 5:2 (1967), 73–78 | DOI | MR | Zbl

[5] Kudaibergenov K. Zh., “Homogeneous models of stable theories”, Siberian Adv. Math., 3:3 (1993), 56–88 | MR

[6] Shelah S., Classification Theory and the Number of Nonisomorphic Models, Studies in Logic and the Foundations of Mathematics, 92, North-Holland Publishing Co., Amsterdam–New York, 1978 | MR | Zbl

[7] Shelah S., “Finite diagrams stable in power”, Ann. Math. Logic, 2:1 (1970), 69–118 | DOI | MR | Zbl