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Weakly quasi-o-minimal models

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Abstract

We introduce the notion of a weakly quasi-o-minimal model and prove that such models lack the independence property. We show that every weakly quasi-o-minimal ordered group is Abelian, every divisible Archimedean weakly quasi-o-minimal ordered group is weakly o-minimal, and every weakly o-minimal quasi-o-minimal ordered group is o-minimal. We also prove that every weakly quasi-o-minimal Archimedean ordered ring with nonzero multiplication is a real closed field that is embeddable into the field of reals.

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Authors and Affiliations

  1. School of General Education, KIMEP, Almaty, 480100, Kazakhstan

    K. Zh. Kudaĭbergenov

Authors
  1. K. Zh. Kudaĭbergenov
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Correspondence to K. Zh. Kudaĭbergenov.

Additional information

Original Russian Text © K. Zh. Kudaĭbergenov, 2010, published in Matematicheskie Trudy, 2010, Vol. 13, No. 1, pp. 156–168.

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Kudaĭbergenov, K.Z. Weakly quasi-o-minimal models. Sib. Adv. Math. 20, 285–292 (2010). https://doi.org/10.3103/S1055134410040036

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  • DOI: https://doi.org/10.3103/S1055134410040036

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