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Algebra Logika, 2004, Volume 43, Number 1, Pages 110–124 (Mi al59)  

This article is cited in 17 scientific papers (total in 17 papers)

Complete Theories with Finitely Many Countable Models. I

S. V. Sudoplatov

Novosibirsk State Technical University

Abstract: A syntactic characterization is furnished for the class of elementary complete theories with finitely many countable models, which is the analog of a known theorem by Ryll-Nardzewski on countably categorical theories, and is based on classifying the theories by Rudin–Keisler quasiorders and distribution functions of a number of models limit over types.

Keywords: elementary complete theory, countable model, Rudin–Keisler quasiorder.

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English version:
Algebra and Logic, 2004, 43:1, 62–69

Bibliographic databases:

UDC: 510.67
Received: 24.10.2001
Revised: 24.04.2002

Citation: S. V. Sudoplatov, “Complete Theories with Finitely Many Countable Models. I”, Algebra Logika, 43:1 (2004), 110–124; Algebra and Logic, 43:1 (2004), 62–69

Citation in format AMSBIB
\by S.~V.~Sudoplatov
\paper Complete Theories with Finitely Many Countable Models.~I
\jour Algebra Logika
\yr 2004
\vol 43
\issue 1
\pages 110--124
\jour Algebra and Logic
\yr 2004
\vol 43
\issue 1
\pages 62--69

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    This publication is cited in the following articles:
    1. S. V. Sudoplatov, “Complete Theories with Finitely Many Countable Models. II”, Algebra and Logic, 45:3 (2006), 180–200  mathnet  crossref  mathscinet  zmath
    2. S. V. Sudoplatov, “Syntactic approach to constructions of generic models”, Algebra and Logic, 46:2 (2007), 134–146  mathnet  crossref  mathscinet  zmath  isi
    3. S. V. Sudoplatov, “Powerful digraphs”, Siberian Math. J., 48:1 (2007), 165–171  mathnet  crossref  mathscinet  zmath  isi
    4. S. V. Sudoplatov, “On the number of countable models of complete theories with finite Rudin–Keisler preorders”, Siberian Math. J., 48:2 (2007), 334–338  mathnet  crossref  mathscinet  zmath  isi
    5. E. N. Pavlovskii, “Slozhnost indeksnykh mnozhestv nekotorykh klassov modelei”, Vestn. NGU. Ser. matem., mekh., inform., 8:1 (2008), 71–76  mathnet
    6. S. V. Sudoplatov, “On expansions and extensions of powerful digraphs”, Siberian Math. J., 50:3 (2009), 498–502  mathnet  crossref  mathscinet  isi
    7. S. V. Sudoplatov, “Hypergraphs of prime models and distributions of countable models of small theories”, J. Math. Sci., 169:5 (2010), 680–695  mathnet  crossref  mathscinet
    8. A. N. Gavryushkin, “O konstruktivnykh modelyakh teorii s lineinym poryadkom Rudina–Keislera”, Vestn. NGU. Ser. matem., mekh., inform., 9:2 (2009), 30–37  mathnet
    9. A. N. Gavryushkin, “Novyi spektr vychislimykh modelei”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 3:4 (2010), 7–20  mathnet
    10. Gavryushkin A., “On Constructive Models of Theories with Linear Rudin-Keisler Ordering”, J. Logic Comput., 22:4, SI (2012), 793–805  crossref  mathscinet  zmath  isi  elib  scopus
    11. I. V. Shulepov, S. V. Sudoplatov, “Algebras of distributions for isolating formulas of a complete theory”, Sib. elektron. matem. izv., 11 (2014), 380–407  mathnet
    12. S. V. Sudoplatov, “O suschestvovanii predelnykh modelei nad posledovatelnostyu tipov”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 9 (2014), 118–133  mathnet
    13. Fokina E.B. Harizanov V. Melnikov A., “Computable Model Theory”, Turing'S Legacy: Developments From Turing'S Ideas in Logic, Lecture Notes in Logic, 42, ed. Downey R., Cambridge Univ Press, 2014, 124–194  mathscinet  isi
    14. R. A. Popkov, S. V. Sudoplatov, “Distributions of countable models of theories with continuum many types”, Sib. elektron. matem. izv., 12 (2015), 267–291  mathnet  crossref
    15. B. Sh. Kulpeshov, S. V. Sudoplatov, “Linearly Ordered Theories which are Nearly Countably Categorical”, Math. Notes, 101:3 (2017), 475–483  mathnet  crossref  crossref  mathscinet  isi  elib
    16. S. V. Sudoplatov, “On distribution of countable models of disjoint unions of Ehrenfeucht theories”, Russian Math. (Iz. VUZ), 62:11 (2018), 76–80  mathnet  crossref  isi
    17. B. Sh. Kulpeshov, S. V. Sudoplatov, “Distributions of countable models of quite $o$-minimal Ehrenfeucht theories”, Eurasian Math. J., 11:3 (2020), 66–78  mathnet  crossref
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