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Matematicheskie Zametki, 2007, Volume 81, Issue 4, Pages 515–527
DOI: https://doi.org/10.4213/mzm3694
(Mi mzm3694)
 

This article is cited in 1 scientific paper (total in 1 paper)

Pseudofinite Homogeneity, Isolation, and Reducibility

S. M. Dudakov

Tver State University
Full-text PDF (499 kB) Citations (1)
References:
Abstract: It has been proved (by S. M. Dudakov and M. A. Taitslin) that the reducibility of some models of a theory implies the second pseudofinite homogeneity property for this theory. We prove the converse, namely, that any theory with the first or the second pseudofinite homogeneity property has a reducible model and, therefore, possesses the second isolation property. This also proves the equivalence of the second isolation property and the second pseudofinite homogeneity property, in contrast to the first pseudofinite homogeneity property, which is more general than the first isolation property (this was established by O. V. Belegradek, A. P. Stolboushin, and M. A. Taitslin).
Keywords: reducible model, first and second pseudofinite homogeneity properties, second isolation property, query language, order collapse property, relational database.
Received: 26.04.2006
English version:
Mathematical Notes, 2007, Volume 81, Issue 4, Pages 456–466
DOI: https://doi.org/10.1134/S0001434607030224
Bibliographic databases:
UDC: 510.675
Language: Russian
Citation: S. M. Dudakov, “Pseudofinite Homogeneity, Isolation, and Reducibility”, Mat. Zametki, 81:4 (2007), 515–527; Math. Notes, 81:4 (2007), 456–466
Citation in format AMSBIB
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\by S.~M.~Dudakov
\paper Pseudofinite Homogeneity, Isolation, and Reducibility
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\vol 81
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\pages 515--527
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\transl
\jour Math. Notes
\yr 2007
\vol 81
\issue 4
\pages 456--466
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Linking options:
  • https://www.mathnet.ru/eng/mzm3694
  • https://doi.org/10.4213/mzm3694
  • https://www.mathnet.ru/eng/mzm/v81/i4/p515
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    Abstract page:336
    Full-text PDF :180
    References:66
    First page:2
     
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