The property of being a model complete theory is preserved by Cartesian extensions

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.