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Algebra Logika, 2011, Volume 50, Number 3, Pages 303–325 (Mi al488)  

This article is cited in 5 scientific papers (total in 5 papers)

$o$-stable theories

B. S. Baizhanova, V. V. Verbovskiib

a Institute of Mathematics, Informatics and Mechanics, Ministry of Education and Science, Alma-Ata, Kazakhstan
b Institute for Problems of Informatics and Control Sciences, Ministry of Education and Science, Alma-Ata, Kazakhstan

Abstract: A well-developed technique created to study stable theories (M. Morley, S. Shelah) is applied in dealing with a class of theories with definable linear order. We introduce the notion of an $o$-stable theory, which generalizes the concepts of $o$-minimality, of weak $o$-minimality, and of quasi-$o$-minimality. It is proved that $o$-stable theories are dependent, but they do not exhaust the class of dependent theories with definable linear order, and that every linear order is $o$-superstable.

Keywords: $o$-stable theory, dependent theory, convex complete 1-type.

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English version:
Algebra and Logic, 2011, 50:3, 211–225

Bibliographic databases:

UDC: 510.67
Received: 18.03.2010

Citation: B. S. Baizhanov, V. V. Verbovskii, “$o$-stable theories”, Algebra Logika, 50:3 (2011), 303–325; Algebra and Logic, 50:3 (2011), 211–225

Citation in format AMSBIB
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\paper $o$-stable theories
\jour Algebra Logika
\yr 2011
\vol 50
\issue 3
\pages 303--325
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\transl
\jour Algebra and Logic
\yr 2011
\vol 50
\issue 3
\pages 211--225
\crossref{https://doi.org/10.1007/s10469-011-9136-7}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. Sh. Kulpeshov, “On self-definable subsets of $\aleph_0$-categorical weakly o-minimal structures”, Sib. elektron. matem. izv., 9 (2012), 433–438  mathnet
    2. V. Verbovskiy, “On a classification of theories without the independence property”, Math. Log. Q., 59:1-2 (2013), 119–124  crossref  mathscinet  zmath  isi  elib  scopus
    3. B. Sh. Kulpeshov, “On connectedness in partially ordered structures”, International Conference on Analysis and Applied Mathematics (ICAAM 2016), AIP Conf. Proc., 1759, eds. A. Ashyralyev, A. Lukashov, Amer. Inst. Phys., 2016, 020062  crossref  isi  scopus
    4. V. V. Verbovskiy, “On ordered groups of Morley o-rank 1”, Sib. elektron. matem. izv., 15 (2018), 314–320  mathnet  crossref
    5. V. V. Verbovskiy, “On commutativity of circularly ordered c-o-stable groups”, Eurasian Math. J., 9:4 (2018), 91–98  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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