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Mat. Tr., 2010, Volume 13, Number 1, Pages 156–168 (Mi mt194)  

This article is cited in 4 scientific papers (total in 4 papers)

Weakly quasi-o-minimal models

K. Zh. Kudaibergenov

School of General Education, KIMEP, Almaty, Kazakhstan

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.

Key words: weakly quasi-o-minimal model, weakly quasi-o-minimal ordered group, weakly quasi-o-minimal ordered ring, the independence property.

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English version:
Siberian Advances in Mathematics, 2010, 20:4, 285–292

Bibliographic databases:

Document Type: Article
UDC: 510.67
Received: 01.09.2009

Citation: K. Zh. Kudaibergenov, “Weakly quasi-o-minimal models”, Mat. Tr., 13:1 (2010), 156–168; Siberian Adv. Math., 20:4 (2010), 285–292

Citation in format AMSBIB
\Bibitem{Kud10}
\by K.~Zh.~Kudaibergenov
\paper Weakly quasi-o-minimal models
\jour Mat. Tr.
\yr 2010
\vol 13
\issue 1
\pages 156--168
\mathnet{http://mi.mathnet.ru/mt194}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2682771}
\transl
\jour Siberian Adv. Math.
\yr 2010
\vol 20
\issue 4
\pages 285--292
\crossref{https://doi.org/10.3103/S1055134410040036}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. Zh. Kudaibergenov, “On the independence property of first order theories and indiscernible sequences”, Siberian Adv. Math., 21:4 (2011), 282–291  mathnet  crossref  mathscinet
    2. K. Zh. Kudaibergenov, “Generalized o-minimality for partial orders”, Siberian Adv. Math., 23:1 (2013), 47–60  mathnet  crossref  mathscinet  elib
    3. Aschenbrenner M., Dolich A., Haskell D., Macpherson D., Starchenko S., “Vapnik-Chervonenkis Density in Some Theories Without the Independence Property, i”, Trans. Am. Math. Soc., 368:8 (2016), 5889–5949  crossref  mathscinet  zmath  isi  elib  scopus
    4. K. Zh. Kudaibergenov, “Otnosheniya vypuklosti i obobscheniya $\mathrm{o}$-minimalnosti”, Matem. tr., 21:1 (2018), 35–54  mathnet  crossref
  • Математические труды Siberian Advances in Mathematics
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