Geodesic
The property of being a model complete theory is preserved by Cartesian extensions
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1540-1551.

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Cartesian-quotient extensions of theories constitute a most common class of finitary transformation methods for first-order combinatorics. In this paper, some technical properties of classes of algebraic Cartesian and algebraic Cartesian-quotient interpretations of theories are studied. It is established that any algebraic Cartesian interpretation preserves the property of being a model complete theory; besides, an example of an algebraic Cartesian-quotient interpretation of theories is given, which does not preserve the model-completeness property.
Keywords: first-order logic, incomplete theory, Tarski-Lindenbaum algebra, model-theoretic property, computable isomorphism, Cartesian interpretation, model completeness. 
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M. G. Peretyat'kin. The property of being a model complete theory is preserved by Cartesian extensions. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1540-1551. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a34/

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