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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 1540–1551
DOI: https://doi.org/10.33048/semi.2020.17.107 (Mi semr1301) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
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DOI: https://doi.org/10.33048/semi.2020.17.107
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.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP05130852
The work was supported by the Ministry of Science and Education of the Republic of Kazakhstan (grant № AP05130852).
Received April 2, 2020, published September 25, 2020
Bibliographic databases:
Document Type: Article
UDC: 510.67
MSC: 03B10,03C10
Language: English
Citation: M. G. Peretyat'kin, “The property of being a model complete theory is preserved by Cartesian extensions”, Sib. Èlektron. Mat. Izv., 17 (2020), 1540–1551
Citation in format AMSBIB
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\by M.~G.~Peretyat'kin
\paper The property of being a model complete theory is preserved by Cartesian extensions
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 1540--1551
\mathnet{http://mi.mathnet.ru/semr1301}
\crossref{https://doi.org/10.33048/semi.2020.17.107}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000575248900001}
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