This article is cited in 2 scientific papers (total in 2 papers)
First-order combinatorics and model-theoretical properties that can be distinct for mutually interpretable theories
M. G. Peretyat'kin
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
The notions of finitary and infinitary combinatorics were recently introduced by the author. In the present article, we discuss these notions and the corresponding semantical layers. We suggest a definition of a model-theoretical property. By author's opinion, this definition agrees with the meaning that is generally accepted and used in model theory. We show that the similarity relation for theories over finitary and infinitary layers of model-theoretical properties is natural and important. Our arguments are based on comparing our approach with known model-theoretical ones. We find examples of pairs of mutually interpretable theories possessing distinct simple model-theoretical properties. These examples show weak points of the notion of mutual interpretability from the point of view of preservation of model-theoretical properties.
first-order logic, theory, Tarski–Lindenbaum algebra, model-theoretical property, interpretation, semantically similar theories, first-order combinatorics.
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Siberian Advances in Mathematics, 2016, 26:3, 196–214
M. G. Peretyat'kin, “First-order combinatorics and model-theoretical properties that can be distinct for mutually interpretable theories”, Mat. Tr., 18:2 (2015), 61–92; Siberian Adv. Math., 26:3 (2016), 196–214
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\paper First-order combinatorics and model-theoretical properties that can be distinct for mutually interpretable theories
\jour Mat. Tr.
\jour Siberian Adv. Math.
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This publication is cited in the following articles:
K. Zh. Kudaibergenov, “On model-theoretical properties in the sense of Peretyat’kin, o-minimality, and mutually interpretable theories”, Siberian Adv. Math., 26:3 (2016), 190–195
M. G. Peretyat'kin, “The property of being a model complete theory is preserved by Cartesian extensions”, Sib. elektron. matem. izv., 17 (2020), 1540–1551
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