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Algebra i logika, 2018, Volume 57, Number 3, Pages 321–337
DOI: https://doi.org/10.17377/alglog.2018.57.305 (Mi al852) 		 
This article is cited in 1 scientific paper (total in 2 paper)

Properties of existentially closed companions

A. T. Nurtazin

Institute of Information and Computational Technologies, Ministry of Education and Science RK, ul. Pushkina 125, Alma-Ata, 050010 Kazakhstan
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DOI: https://doi.org/10.17377/alglog.2018.57.305
Abstract: Necessary and sufficient conditions are stated for an arbitrary theory to be an elementary theory for a class of its existentially closed models. Conditions are given under which some existentially closed model simultaneously realizes one maximal existential type and omits another. We also prove a theorem on a prime existentially closed model over a maximal existential type. Considerable complexity of existentially closed structures and their theories was noted by A. Macintyre. Therefore, the examples of existentially closed companions having any finite or countable number of pairwise non elementarily equivalent existentially closed models constructed here are of interest.
Keywords: elementary theory, existentially closed model, existentially closed companion, existential type.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan 0174/ГФ4
Supported by KN MON RK, project No. 0174/GF4.
Received: 06.01.2017
Revised: 25.10.2017
English version:
Algebra and Logic, 2018, Volume 57, Issue 3, Pages 211–221
DOI: https://doi.org/10.1007/s10469-018-9494-5
Bibliographic databases:
Document Type: Article
UDC: 510.8
Language: Russian
Citation: A. T. Nurtazin, “Properties of existentially closed companions”, Algebra Logika, 57:3 (2018), 321–337; Algebra and Logic, 57:3 (2018), 211–221
Citation in format AMSBIB
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\by A.~T.~Nurtazin
\paper Properties of existentially closed companions
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\issue 3
\pages 321--337
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\issue 3
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    • This publication is cited in the following 2 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 :98
    References:33
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