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Algebra Logika, 2012, Volume 51, Number 6, Pages 748–765 (Mi al562)  

This article is cited in 2 scientific papers (total in 2 papers)

Existentially closed and maximal models in positive logic

A. Kungozhin

Al-Farabi Kazakh National University, Alma-Ata, Kazakhstan

Abstract: It is proved that a subclass of positively existentially closed models of any finitely axiomatizable $h$-universal class in a predicate signature is axiomatizable. We construct examples suggesting the necessity of these conditions for the given subclass to be axiomatizable. The concept of an $h$-maximal model is introduced. It is shown that a subclass of $h$-maximal models of any finitely axiomatizable $h$-universal class is also finitely axiomatizable. Moreover, the set of positively existentially closed models in an $h$-universally axiomatizable class coincides with the set of positively existentially closed models in its subclass of $h$-maximal models.

Keywords: finitely axiomatizable $h$-universal class, positively existentially closed model.

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English version:
Algebra and Logic, 2013, 51:6, 496–506

Bibliographic databases:

UDC: 510.67
Received: 07.03.2012
Revised: 10.10.2012

Citation: A. Kungozhin, “Existentially closed and maximal models in positive logic”, Algebra Logika, 51:6 (2012), 748–765; Algebra and Logic, 51:6 (2013), 496–506

Citation in format AMSBIB
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\by A.~Kungozhin
\paper Existentially closed and maximal models in positive logic
\jour Algebra Logika
\yr 2012
\vol 51
\issue 6
\pages 748--765
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\zmath{https://zbmath.org/?q=an:06189470}
\transl
\jour Algebra and Logic
\yr 2013
\vol 51
\issue 6
\pages 496--506
\crossref{https://doi.org/10.1007/s10469-013-9209-x}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84880698689}


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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. Belkasmi M., “Positive Model Theory and Amalgamations”, Notre Dame J. Form. Log., 55:2 (2014), 205–230  crossref  mathscinet  zmath  isi  elib  scopus
    2. Poizat B., Yeshkeyev A., “Positive Jonsson Theories”, Log Universalis, 12:1-2 (2018), 101–127  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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