Geodesic
Weakly quasi-o-minimal models
Matematičeskie trudy, Tome 13 (2010) no. 1, pp. 156-168.

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We introduce the notion of a weakly quasi-o-minimal model and prove that such models lack the independence property. We show that every weakly quasi-o-minimal ordered group is Abelian, every divisible Archimedean weakly quasi-o-minimal ordered group is weakly o-minimal, and every weakly o-minimal quasi-o-minimal ordered group is o-minimal. We also prove that every weakly quasi-o-minimal Archimedean ordered ring with nonzero multiplication is a real closed field that is embeddable into the field of reals. 
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K. Zh. Kudaibergenov. Weakly quasi-o-minimal models. Matematičeskie trudy, Tome 13 (2010) no. 1, pp. 156-168. http://geodesic.mathdoc.fr/item/MT_2010_13_1_a6/

[1] Melnikov O. V., Remeslennikov V. N., Romankov V. A., Skornyakov L. A., Shestakov I. P., Obschaya algebra, v. 1, Nauka, M., 1990

[2] Belegradek O., Peterzil Y., Wagner F., “Quasi-o-minimal structures”, J. Symbolic Logic, 65:3 (2000), 1115–1132 | DOI | MR | Zbl

[3] Belegradek O. V., Stolboushkin A. P., Taitslin M. A., “Generic queries over quasi-o-minimal domains”, Logical Foundations of Computer Science (Yaroslavl, 199), Lecture Notes in Comput. Sci., 1234, Springer-Verlag, Berlin, 1997, 21–32 | MR | Zbl

[4] Dickmann M. A., “Elimination of quantifiers for ordered valuation rings”, Proc. of the 3rd Easter Conf. on Model Theory (Gross Koris, 1985), Seminarberichte, 70, Humboldt Univ., Berlin, 1985, 64–88 | MR | Zbl

[5] Kudaibergenov K. Zh., “Remarks on weak o-minimality”, Vestnik SDU, 2008, no. 3, 95–98

[6] Macpherson D., Marker D., Steinhorn C., “Weakly o-minimal structures and real closed fields”, Trans. Amer. Math. Soc., 352:12 (2000), 5435–5483 | DOI | MR | Zbl

[7] Pillay A., Steinhorn C., “Definable sets in ordered structures. I”, Trans. Amer. Math. Soc., 295:2 (1986), 565–592 | DOI | MR | Zbl

[8] Poizat B., “Théories instables”, J. Symbolic Logic, 46 (1981), 513–522 | DOI | MR | Zbl

[9] 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