Skip to main content
SpringerLink
Log in

Small stable generic graphs with infinite weight. Digraphs without furcations

  • Published:
Siberian Advances in Mathematics Aims and scope Submit manuscript

Abstract

Grounding on Herwig’s generic construction that modifies Hrushovski’s construction, we give some examples of small stable theories of digraphs without furcations which have an infinite weight.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baldwin J. T. and Shi N., “Stable generic structures,” Ann. Pure Appl. Logic 79, 1–35 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  2. Barwise J., Ershov Yu. L., Palyutin E. A., and Taĭmanov A. D., eds., Model Theory, vol. 1 of Handbook of Mathematical Logic (Nauka, Moscow, 1982) [in Russian].

    Google Scholar 

  3. Herwig B., “Weight ω in stable theories with few types,” J. Symbolic Logic 60(2), 353–373 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  4. Hrushovski E., A Stable ℵ 0-Categorical Pseudoplane, Preprint (Hebrew University, Jerusalem, 1988).

    Google Scholar 

  5. Shelah S., Classification Theory and the Number of Nonisomorphic Models, vol. 92 of Studies in Logic and the Foundations of Mathematics (North-Holland, Amsterdam, 1990).

    Google Scholar 

  6. Sudoplatov S. V., “Complete theories with finitely many countable models. II,” Algebra i Logika 45(3) 314–353, 375–376 (2006) [Algebra and Logic 45 (3), 180–200 (2006)].

    MATH  MathSciNet  Google Scholar 

  7. Sudoplatov S. V., “Small stable generic graphs with infinite weight. Bipartite digraphs,” Mat. Tr. 9(2), 154–171 (2006) [Siberian Adv. Math. 17 (1), 37–48 (2007)].

    MathSciNet  Google Scholar 

  8. Sudoplatov S. V., “Powerful digraphs,” Sibirsk. Mat. Zh. 48(1), 205–213 (2007) [Siberian Math. J. 48 (1), 165–171 (2007)].

    MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  10. Sudoplatov S. V. and Ovchinnikova E. V., Discrete Mathematics (INFRA-M, Moscow, 2005).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    S. V. Sudoplatov

Authors
  1. S. V. Sudoplatov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. V. Sudoplatov.

Additional information

Original Russian Text © S. V. Sudoplatov, 2007, published in Matermaticheskie Trudy, 2007, Vol. 10, No. 1, pp. 191–207.

About this article

Cite this article

Sudoplatov, S.V. Small stable generic graphs with infinite weight. Digraphs without furcations. Sib. Adv. Math. 18, 142–151 (2008). https://doi.org/10.3103/S1055134408020077

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1055134408020077

Key words

Search

Navigation