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Mat. Tr., 2015, Volume 18, Number 2, Pages 61–92 (Mi mt294)  

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

Abstract: 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.

Key words: first-order logic, theory, Tarski–Lindenbaum algebra, model-theoretical property, interpretation, semantically similar theories, first-order combinatorics.

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan 0767/ГФ


DOI: https://doi.org/10.17377/mattrudy.2015.18.205

Full text: PDF file (522 kB)
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English version:
Siberian Advances in Mathematics, 2016, 26:3, 196–214

Bibliographic databases:

UDC: 510.6
Received: 10.02.2014

Citation: 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

Citation in format AMSBIB
\Bibitem{Per15}
\by M.~G.~Peretyat'kin
\paper First-order combinatorics and model-theoretical properties that can be distinct for mutually interpretable theories
\jour Mat. Tr.
\yr 2015
\vol 18
\issue 2
\pages 61--92
\mathnet{http://mi.mathnet.ru/mt294}
\crossref{https://doi.org/10.17377/mattrudy.2015.18.205}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3588292}
\elib{https://elibrary.ru/item.asp?id=24639781}
\transl
\jour Siberian Adv. Math.
\yr 2016
\vol 26
\issue 3
\pages 196--214
\crossref{https://doi.org/10.3103/S1055134416030044}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  elib
    2. 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  mathnet  crossref
  • Математические труды Siberian Advances in Mathematics
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