On model-theoretical properties in the sense of Peretyat’kin, o-minimality, and mutually interpretable theories
Matematičeskie trudy, Tome 18 (2015) no. 2, pp. 39-48.

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We prove that o-minimality is not a model-theoretical property in the sense of Peretyat’kin. We also prove that existence of a prime models need not be preserved under a passage between mutually interpretable theories.
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K. Zh. Kudaibergenov. On model-theoretical properties in the sense of Peretyat’kin, o-minimality, and mutually interpretable theories. Matematičeskie trudy, Tome 18 (2015) no. 2, pp. 39-48. http://geodesic.mathdoc.fr/item/MT_2015_18_2_a2/

[1] Ershov Yu. L., Palyutin E. A., Matematicheskaya logika, Nauka, M., 1987

[2] Keisler G., Chen Ch. Ch., Teoriya modelei, Mir, M., 1977

[3] Peretyatkin M. G., “Kombinatorika pervogo poryadka i teoretiko-modelnye svoistva, razlichimye na parakh vzaimno interpretiruemykh teorii”, Matem. tr., 18:2 (2015), 61–92

[4] Shenfild Dzh., Matematicheskaya logika, Nauka, M., 1975

[5] Knight J., Pillay A., Steinhorn C., “Definable sets in ordered structures, II”, Trans. Amer. Math. Soc., 295:2 (1986), 593–605 | DOI | Zbl

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

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

[8] 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