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Fundam. Prikl. Mat., 2009, Volume 15, Issue 7, Pages 179–203 (Mi fpm1277)  

This article is cited in 5 scientific papers (total in 5 papers)

Hypergraphs of prime models and distributions of countable models of small theories

S. V. Sudoplatov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Hypergraphs of prime models over realizations of types in small theories are defined. On the basis of graph structures of models of small theories, hierarchies of sets in these hypergraphs, revealing structural connections in countable models of small theories, are established. The key role of graph-theoretic objects in constructions of Ehrenfeucht theories is proved. Using hypergraph constructions, a classification of complete first-order theories with finite Rudin–Keisler preorders is generalized to the class of all small theories.

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English version:
Journal of Mathematical Sciences (New York), 2010, 169:5, 680–695

Bibliographic databases:

UDC: 510.67

Citation: S. V. Sudoplatov, “Hypergraphs of prime models and distributions of countable models of small theories”, Fundam. Prikl. Mat., 15:7 (2009), 179–203; J. Math. Sci., 169:5 (2010), 680–695

Citation in format AMSBIB
\Bibitem{Sud09}
\by S.~V.~Sudoplatov
\paper Hypergraphs of prime models and distributions of countable models of small theories
\jour Fundam. Prikl. Mat.
\yr 2009
\vol 15
\issue 7
\pages 179--203
\mathnet{http://mi.mathnet.ru/fpm1277}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2745009}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 169
\issue 5
\pages 680--695
\crossref{https://doi.org/10.1007/s10958-010-0069-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77956060057}


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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. S. V. Sudoplatov, “O predelnykh modelyakh nad tipom v klasse $\omega$-stabilnykh teorii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 3:4 (2010), 114–120  mathnet
    2. S. V. Sudoplatov, “O suschestvovanii predelnykh modelei nad posledovatelnostyu tipov”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 9 (2014), 118–133  mathnet
    3. D. Yu. Emel'yanov, B. Sh. Kulpeshov, S. V. Sudoplatov, “Algebras of distributions for binary formulas in countably categorical weakly $o$-minimal structures”, Algebra and Logic, 56:1 (2017), 13–36  mathnet  crossref  crossref  isi
    4. S. V. Sudoplatov, “O raspredeleniyakh schetnykh modelei diz'yunktnykh ob'edinenii erenfoikhtovykh teorii”, Izv. vuzov. Matem., 2018, no. 11, 86–91  mathnet
    5. B. Sh. Kulpeshov, S. V. Sudoplatov, “On relative separability in hypergraphs of models of theories”, Eurasian Math. J., 9:4 (2018), 68–78  mathnet  crossref
  • Фундаментальная и прикладная математика
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