Skip to main content

On the definition of the small index property


For countable infinite structures, two definitions of the small index property are known. One of them contains the words “at most ω,” while the other reads “less than 2ω.” In the present article, we explain in what sense there is no big difference between the two definitions and suggest a generalization to arbitrary infinite structures.

This is a preview of subscription content, access via your institution.


  1. 1.

    J. P. Burgess, “Forcing,” in Handbook of Mathematical Logic (North-Holland, Amsterdam, 1977), 403.

    Chapter  Google Scholar 

  2. 2.

    W. Hodges, Model Theory (Cambridge University Press, Cambridge, 1993).

    Book  MATH  Google Scholar 

  3. 3.

    D. Lascar and S. Shelah, “Uncountable saturated structures have the small index property,” Bull. London Math. Soc. 25, 125 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  4. 4.

    D. Macpherson, “A survey of homogeneous structures,” Discrete Math. 311, 1599 (2011).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to K. Zh. Kudaĭbergenov.

Additional information

Original Russian Text © K.Zh. Kudaĭbergenov, 2014, published in Matematicheskie Trudy, 2014, Vol. 17, No. 1, pp. 123–127.

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kudaĭbergenov, K.Z. On the definition of the small index property. Sib. Adv. Math. 25, 206–208 (2015).

Download citation


  • small index property