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Matematicheskie Trudy, 2010, Volume 13, Number 1, Pages 156–168 (Mi mt194)  
This article is cited in 9 scientific papers (total in 9 papers)

Weakly quasi-o-minimal models

K. Zh. Kudaibergenov

School of General Education, KIMEP, Almaty, Kazakhstan
Full-text PDF (191 kB) Citations (9)
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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.
Key words: weakly quasi-o-minimal model, weakly quasi-o-minimal ordered group, weakly quasi-o-minimal ordered ring, the independence property.
Received: 01.09.2009
English version:
Siberian Advances in Mathematics, 2010, Volume 20, Issue 4, Pages 285–292
DOI: https://doi.org/10.3103/S1055134410040036
Bibliographic databases:
Document Type: Article
UDC: 510.67
Language: Russian
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://mathscinet.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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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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