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On the definition of the small index property

Abstract

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.

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Correspondence to K. Zh. Kudaĭbergenov.

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

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Kudaĭbergenov, K.Z. On the definition of the small index property. Sib. Adv. Math. 25, 206–208 (2015). https://doi.org/10.3103/S1055134415030050

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Keywords

  • small index property