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On model-theoretical properties in the sense of Peretyat’kin, o-minimality, and mutually interpretable theories

Abstract

We prove that o-minimality is not a model-theoretical property in the sense of Peretyat’kin. We also prove that existence of a prime models need not be preserved under a passage between mutually interpretable theories.

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Correspondence to K. Zh. Kudaĭbergenov.

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Original Russian Text © K.Zh. Kuda˘ıbergenov, 2015, published in Matematicheskie Trudy, 2015, Vol. 18, No. 2, pp. 39–48.

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Kudaĭbergenov, K.Z. On model-theoretical properties in the sense of Peretyat’kin, o-minimality, and mutually interpretable theories. Sib. Adv. Math. 26, 190–195 (2016). https://doi.org/10.3103/S1055134416030032

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Keywords

  • model-theoretical properties
  • mutually interpretable theories