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Algebra Logika, 2011, Volume 50, Number 5, Pages 659–684 (Mi al507)  

This article is cited in 6 scientific papers (total in 6 papers)

$\Sigma$-uniform structures and $\Sigma$-functions. I

A. N. Khisamiev

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

Abstract: The concept of a $\Sigma$-uniform structure is introduced. A condition is derived which is necessary and sufficient for a universal $\Sigma$-function to exist in a hereditarily finite admissible set over a $\Sigma$-uniform structure.

Keywords: hereditarily finite admissible set, $\Sigma$-definability, universal $\Sigma$-function, $\Sigma$-uniform structure.

Full text: PDF file (271 kB)
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English version:
Algebra and Logic, 2011, 50:5, 447–465

Bibliographic databases:

UDC: 512.540+510.5
Received: 24.11.2010
Revised: 05.06.2011

Citation: A. N. Khisamiev, “$\Sigma$-uniform structures and $\Sigma$-functions. I”, Algebra Logika, 50:5 (2011), 659–684; Algebra and Logic, 50:5 (2011), 447–465

Citation in format AMSBIB
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\by A.~N.~Khisamiev
\paper $\Sigma$-uniform structures and $\Sigma$-functions.~I
\jour Algebra Logika
\yr 2011
\vol 50
\issue 5
\pages 659--684
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2907412}
\zmath{https://zbmath.org/?q=an:06115017}
\transl
\jour Algebra and Logic
\yr 2011
\vol 50
\issue 5
\pages 447--465
\crossref{https://doi.org/10.1007/s10469-011-9155-4}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-82955233141}


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    Citing articles on Google Scholar: Russian citations, English citations
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    Cycle of papers

    This publication is cited in the following articles:
    1. A. N. Khisamiev, “$\Sigma$-uniform structures and $\Sigma$-functions. II”, Algebra and Logic, 51:1 (2012), 89–102  mathnet  crossref  mathscinet  zmath  isi
    2. S. A. Aleksandrova, “The uniformization problem for $\Sigma$-predicates in a hereditarily finite list superstructure over the real exponential field”, Algebra and Logic, 53:1 (2014), 1–8  mathnet  crossref  mathscinet  isi
    3. A. N. Khisamiev, “Universal functions and almost $c$-simple models”, Siberian Math. J., 56:3 (2015), 526–540  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. A. N. Khisamiev, “Universal functions over trees”, Algebra and Logic, 54:2 (2015), 188–193  mathnet  crossref  crossref  mathscinet  isi
    5. A. N. Khisamiev, “A class of almost $c$-simple rings”, Siberian Math. J., 56:6 (2015), 1133–1141  mathnet  crossref  crossref  mathscinet  isi  elib
    6. A. N. Khisamiev, “Universal functions and unbounded branching trees”, Algebra and Logic, 57:4 (2018), 309–319  mathnet  crossref  crossref  isi
  • Алгебра и логика Algebra and Logic
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