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Algebra i logika, 2007, Volume 46, Number 2, Pages 244–268 (Mi al4)  
This article is cited in 15 scientific papers (total in 15 papers)

Syntactic approach to constructions of generic models

S. V. Sudoplatov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (265 kB) Citations (15)
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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.
Received: 24.09.2005
English version:
Algebra and Logic, 2007, Volume 46, Issue 2, Pages 134–146
DOI: https://doi.org/10.1007/s10469-007-0012-4
Bibliographic databases:
UDC: 510.67
Language: Russian
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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\jour Algebra Logika
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\pages 244--268
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\issue 2
\pages 134--146
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Linking options:
  • https://www.mathnet.ru/eng/al4
  • https://www.mathnet.ru/eng/al/v46/i2/p244
    • This publication is cited in the following 15 articles:
    1. S. V. Sudoplatov, “Arities and aritizabilities of first-order theories”, Sib. elektron. matem. izv., 19:2 (2022), 889–901  mathnet  crossref  mathscinet
    2. S. V. Sudoplatov, “Spectra for Generative Classes”, Sib. Adv. Math., 31:1 (2021), 53  crossref
    3. Y. Kiouvrekis, P. Stefaneas, S. V. Sudoplatov, “Lattices in generative classes”, Sib. elektron. matem. izv., 16 (2019), 1752–1761  mathnet  crossref
    4. A. Yu. Mikhaylenko, S. V. Sudoplatov, “Conflict and conflict-free theories”, Sib. elektron. matem. izv., 16 (2019), 1833–1842  mathnet  crossref
    5. Sudoplatov S.V., “On Generic Structures Preserving Elementary Equivalence and Elementary Embeddability”, Bull. Karaganda Univ-Math., 89:1 (2018), 70–76  isi
    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. 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, “On expansions and extensions of powerful digraphs”, Siberian Math. J., 50:3 (2009), 498–502  mathnet  crossref  mathscinet  isi
    13. 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
    14. S. V. Sudoplatov, “Small Stable Generic Graphs with Infinite Weight. Digraphs without Furcations”, Siberian Adv. Math., 18:2 (2008), 142–150  mathnet  crossref  mathscinet
    15. S. V. Sudoplatov, “Small Stable Generic Graphs with Infinite Weight. Bipartite Digraphs”, Siberian Adv. Math., 17:1 (2007), 37–48  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и логика Algebra and Logic
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