This article is cited in 1 paper

Mathematical logic, algebra and number theory

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

M. G. Peretyat'kin

Institute of Mathematics and Mathematical Modeling, 125, Pushkin str., Almaty, 050010, Kazakhstan

Abstract: 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.

UDC: 510.67

MSC: 03B10,03C10

Received April 2, 2020, published September 25, 2020

Language: English

DOI: 10.33048/semi.2020.17.107

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