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Mat. Tr., 2009, Volume 12, Number 2, Pages 97–110 (Mi mt182)  

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

Cardinalities of definable sets in superstructures over models

K. Zh. Kudaibergenov

Department of Economics, Kazakhstan Institute of Management, Economics and Strategic Research, Almaty, Kazakhstan

Abstract: We introduce the notion of a superstructure over a model. This is a generalization of the notion of the hereditarily finite superstructure $\mathbb{HF}(\mathfrak M)$ over a model $\mathfrak M$. We consider the question on cardinalities of definable (interpretable) sets in superstructures over $\lambda$-homogeneous and $\lambda$-saturated models.

Key words: superstructure over a model, definable set, homogeneous model, saturated model.

Full text: PDF file (221 kB)
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English version:
Siberian Advances in Mathematics, 2010, 20:1, 58–67

Bibliographic databases:

UDC: 510.67
Received: 18.01.2009

Citation: K. Zh. Kudaibergenov, “Cardinalities of definable sets in superstructures over models”, Mat. Tr., 12:2 (2009), 97–110; Siberian Adv. Math., 20:1 (2010), 58–67

Citation in format AMSBIB
\Bibitem{Kud09}
\by K.~Zh.~Kudaibergenov
\paper Cardinalities of definable sets in superstructures over models
\jour Mat. Tr.
\yr 2009
\vol 12
\issue 2
\pages 97--110
\mathnet{http://mi.mathnet.ru/mt182}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2599426}
\transl
\jour Siberian Adv. Math.
\yr 2010
\vol 20
\issue 1
\pages 58--67
\crossref{https://doi.org/10.3103/S1055134410010025}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Vasilev, “Krainie tochki mnogogrannika Vebera”, Diskretn. analiz i issled. oper., ser. 1, ser. 1, 10:2 (2003), 17–55  mathnet  mathscinet  zmath
    2. I. Kiouvrekis, P. Stefaneas, S. V. Sudoplatov, “Definable sets in generic structures and their cardinalities”, Siberian Adv. Math., 28:1 (2018), 39–52  mathnet  crossref  crossref  elib
  • Математические труды Siberian Advances in Mathematics
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