Advertisement

Archive for Mathematical Logic

, Volume 57, Issue 7–8, pp 769–794 | Cite as

Model completeness of generic graphs in rational cases

  • Hirotaka KikyoEmail author
Article
  • 37 Downloads

Abstract

Let \(\mathbf {K}_f\) be an ab initio amalgamation class with an unbounded increasing concave function f. We show that if the predimension function has a rational coefficient and f satisfies a certain assumption then the generic structure of \(\mathbf {K}_f\) has a model complete theory.

Keywords

Hrushovski’s amalgamation construction Model completeness 

Mathematics Subject Classification

03C10 03C13 03C25 03C30 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The author appreciates valuable discussions with Koichiro Ikeda, Akito Tsuboi, Masanori Sawa, and Genki Tatsumi. The author also would like to appreciate the referee for the valuable comments. The author is supported by JSPS KAKENHI Grant Nos. 25400203 and 17K05345.

References

  1. 1.
    Baldwin, J.T., Holland, K.: Constructing \(\omega \)-stable structures: model completeness. Ann. Pure Appl. Log. 125, 159–172 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Baldwin, J.T., Shelah, S.: Randomness and semigenericity. Trans. Am. Math. Soc. 349, 1359–1376 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Baldwin, J.T., Shi, N.: Stable generic structures. Ann. Pure Appl. Log. 79, 1–35 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Diestel, R.: Graph Theory, 4th edn. Springer, New York (2010)CrossRefzbMATHGoogle Scholar
  5. 5.
    Holland, K.: Model completeness of the new strongly minimal sets. J. Symb. Log. 64, 946–962 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Hrushovski, E.: A stable \(\aleph _0\)-categorical pseudoplane (preprint) (1988)Google Scholar
  7. 7.
    Hrushovski, E.: A new strongly minimal set. Ann. Pure Appl. Log. 62, 147–166 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Ikeda, K., Kikyo, H.: Model complete generic structures. In: The Proceedings of the 13th Asian Logic Conference, World Scientific, pp. 114–123 (2015)Google Scholar
  9. 9.
    Kikyo, H.: Model complete generic graphs I. RIMS Kokyuroku 1938, 15–25 (2015)Google Scholar
  10. 10.
    Kikyo, H.: Balanced zero-sum sequences and minimal intrinsic extensions. RIMS Kokyuroku (to appear)Google Scholar
  11. 11.
    Wagner, F.O.: Relational Structures and Dimensions, in Automorphisms of First-Order Structures, pp. 153–181. Clarendon Press, Oxford (1994)zbMATHGoogle Scholar
  12. 12.
    Wagner, F.O.: Simple Theories. Kluwer, Dordrecht (2000)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Graduate School of System InformaticsKobe UniversityKobeJapan

Personalised recommendations