Skip to main content
SpringerLink
Log in

On constants and the strict order property

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract

Let T be a complete, countable, first-order theory with a finite number of countable models. Assuming that dcl(∅) is infinite we show that T has the strict order property.

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. Herwig, B., Loveys, J., Pillay, A., Tanović, P., Wagner, F.O.: Stable theories with no dense forking chains. Arch. Math. Logic 31, pp. 297–302 (1992)

    Google Scholar 

  2. Hrushovski, E.: Finitely based theories. J. Symb. Logic 54, pp. 221–225 (1989)

  3. Lachlan, A.: On the number of countable models of a superstable theory. Logic, Methodology and Philosophy of Science. P. Suppes et al.(eds), North-Holland, 1973, pp. 45–56

  4. Loveys, J., Tanović P.: Countable models of trivial theories which admit finite coding. J. Symb. Logic 61, pp. 1279–1286 (1996)

    Google Scholar 

  5. Pertyatkin, M.G.: On complete theories with a finite number of countable models(in Russian). Algebra i Logika 12, pp. 550–576 (1973)

  6. Pertyatkin, M.G.: On theories with three countable models(in Russian). Algebra i Logika 19, pp. 224–235 (1980)

  7. Pillay, A.: Number of countable models. J. Symb. Logic 43, pp. 494–496 (1978)

  8. Pillay, A.: Dimension theory and homogeneity for elementary extensions of a model. J. Symb. Logic 47, pp. 147–160 (1982)

    Google Scholar 

  9. Pillay, A.: Stable theories, pseudoplanes and the number of countable models. Ann. Pure Appl. Logic 43, pp. 147–160 (1989)

    Google Scholar 

  10. Tanović, P.: Fundamental Order and the Number of Countable Models. PhD Thesis, McGill University, 1993

  11. Tanović, P.: On the number of countable models of stable theories. Fund. Math. 169, pp. 139–144 (2001)

    Google Scholar 

  12. Tsuboi, A.: On theories having a finite number of non-isomorphic countable models. J. Symb. Logic 50, pp. 806–808 (1985)

    Google Scholar 

  13. Vaught, R.L.: Denumerable models of complete theories. In: Infinitistic Methods. Proceedings of the Symposium on Foundations of Mathematics. Panstwowe Wydawnictvo Naukowe, 1961, pp. 303–321

  14. Woodrow, R.E.: Theories with a finite number of countable models. J. Symb. Logic 43, pp. 442–455 (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Matematički Institut SANU, Knez Mihajlova 35, 11001, Beograd, Serbia and Montenegro

    Predrag Tanović

Authors
  1. Predrag Tanović
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Predrag Tanović.

Additional information

The author is supported by Ministry of Science and Technology of Serbia

Thanks to the referee for the comments; thanks to Anand Pillay and the referee for a very quick procession of the paper.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tanović, P. On constants and the strict order property. Arch. Math. Logic 45, 423–430 (2006). https://doi.org/10.1007/s00153-005-0323-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-005-0323-x

Mathematics Subject Classification (2000)

Search

Navigation