Geodesic
Cardinalities of definable sets in superstructures over models
Matematičeskie trudy, Tome 12 (2009) no. 2, pp. 97-110.

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We introduce the notion of a superstructure over a model. This is a generalization of the notion of the hereditarily finite superstructure $\mathbb{HF}(\mathfrak M)$ over a model $\mathfrak M$. We consider the question on cardinalities of definable (interpretable) sets in superstructures over $\lambda$-homogeneous and $\lambda$-saturated models. 
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K. Zh. Kudaibergenov. Cardinalities of definable sets in superstructures over models. Matematičeskie trudy, Tome 12 (2009) no. 2, pp. 97-110. http://geodesic.mathdoc.fr/item/MT_2009_12_2_a3/

[1] Ershov Yu. L., Opredelimost i vychislimost, Ekonomika, M.; Nauchnaya kniga, Novosibirsk, 2000 | MR

[2] Keisler Kh. Dzh., “Osnovy teorii modelei”, Spravochnaya kniga po matematicheskoi logike, Ch. 1. Teoriya modelei, Nauka, M., 1982, 55–108 | MR

[3] Kudaibergenov K. Zh., “Ob odnoi gipoteze Shelakha”, Algebra i logika, 26:2 (1987), 191–203 | MR

[4] Kudaibergenov K. Zh., “Ob odnorodnosti i malykh rasshireniyakh modelei teorii lineinogo poryadka”, Mat. trudy, 11:2 (2008), 148–158 | MR

[5] Saks Dzh., Teoriya nasyschennykh modelei, Mir, M., 1976 | MR

[6] Carp C., Languages with Expressions of Infinite Length, North-Holland, Amsterdam, 1964 | MR

[7] Ellentuck E., “Categoricity revisited”, J. Symbolic Logic, 41:3 (1976), 639–643 | DOI | MR | Zbl

[8] 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

[9] Shelah S., Classification Theory and the Number of Nonisomorphic Models, North-Holland, Amsterdam, 1978 | MR | Zbl