Geodesic
$\Sigma$-Definability in Hereditarily Finite Superstructures and Pairs of Models
Algebra i logika, Tome 43 (2004) no. 4, pp. 459-481.

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We consider the problem of being $\Sigma$-definable for an uncountable model of a $c$-simple theory in hereditarily finite superstructures over models of another $c$-simple theory. A necessary condition is specified in terms of decidable models and the concept of relative indiscernibility introduced in the paper. A criterion is stated for the uncountable model of a $c$-simple theory to be $\Sigma$-definable in superstructures over dense linear orders, and over infinite models of the empty signature. We prove the existence of a $c$-simple theory (of an infinite signature) every uncountable model of which is not $\Sigma$-definable in superstructures over dense linear orders. Also, a criterion is given for a pair of models to be recursively saturated.
Keywords: $\Sigma$-definability, $c$-simple theory, model, hereditarily finite superstructure, linear order. 
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A. I. Stukachev. $\Sigma$-Definability in Hereditarily Finite Superstructures and Pairs of Models. Algebra i logika, Tome 43 (2004) no. 4, pp. 459-481. http://geodesic.mathdoc.fr/item/AL_2004_43_4_a4/

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