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Algebra i logika, 2011, Volume 50, Number 3, Pages 303–325 (Mi al488)  
This article is cited in 10 scientific papers (total in 11 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
Full-text PDF (240 kB) Citations (11)
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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.
Received: 18.03.2010
English version:
Algebra and Logic, 2011, Volume 50, Issue 3, Pages 211–225
DOI: https://doi.org/10.1007/s10469-011-9136-7
Bibliographic databases:
Document Type: Article
UDC: 510.67
Language: Russian
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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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и логика Algebra and Logic
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    Full-text PDF :128
    References:72
    First page:11
     
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