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Algebra Logika, 2007, Volume 46, Number 2, Pages 244–268 (Mi al4)  

This article is cited in 11 scientific papers (total in 11 papers)

Syntactic approach to constructions of generic models

S. V. Sudoplatov

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

Abstract: A syntactic approach is described to constructing generic models which generalizes the known semantic one. A sufficient condition of a generic model being homogeneous is specified. It is shown that, within the syntactic approach, any countable homogeneous model is generic. Criteria and a sufficient condition are given for the generic models created in syntactic constructions to be saturated.

Keywords: generic model, generic theory.

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English version:
Algebra and Logic, 2007, 46:2, 134–146

Bibliographic databases:

UDC: 510.67
Received: 24.09.2005

Citation: S. V. Sudoplatov, “Syntactic approach to constructions of generic models”, Algebra Logika, 46:2 (2007), 244–268; Algebra and Logic, 46:2 (2007), 134–146

Citation in format AMSBIB
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\paper Syntactic approach to constructions of generic models
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\issue 2
\pages 244--268
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\yr 2007
\vol 46
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\pages 134--146
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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, “Small Stable Generic Graphs with Infinite Weight. Bipartite Digraphs”, Siberian Adv. Math., 17:1 (2007), 37–48  mathnet  crossref  mathscinet
    2. S. V. Sudoplatov, “Small Stable Generic Graphs with Infinite Weight. Digraphs without Furcations”, Siberian Adv. Math., 18:2 (2008), 142–150  mathnet  crossref  mathscinet
    3. S. V. Sudoplatov, “On expansions and extensions of powerful digraphs”, Siberian Math. J., 50:3 (2009), 498–502  mathnet  crossref  mathscinet  isi
    4. 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
    5. 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
    6. 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
    7. S. V. Sudoplatov, “Combinations related to classes of finite and countably categorical structures and their theories”, Sib. elektron. matem. izv., 14 (2017), 135–150  mathnet  crossref
    8. I. Kiouvrekis, P. Stefaneas, S. V. Sudoplatov, “Definable sets in generic structures and their cardinalities”, Siberian Adv. Math., 28:1 (2018), 39–52  mathnet  crossref  crossref  elib
    9. S. V. Sudoplatov, “Generations of generative classes”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 22 (2017), 106–117  mathnet  crossref
    10. Sudoplatov S.V., Kiouvrekis Y., Stefaneas P., “Generic Constructions and Generic Limits”, Algebraic Modeling of Topological and Computational Structures and Applications, Springer Proceedings in Mathematics & Statistics, 219, eds. Lambropoulou S., Theodorou D., Stefaneas P., Kauffman L., Springer, 2017, 375–398  crossref  mathscinet  zmath  isi  scopus
    11. Sudoplatov S.V., “On Generic Structures Preserving Elementary Equivalence and Elementary Embeddability”, Bull. Karaganda Univ-Math., 89:1 (2018), 70–76  isi
  • Алгебра и логика Algebra and Logic
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