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Algebra Logika, 2012, Volume 51, Number 1, Pages 129–147 (Mi al525)  

This article is cited in 4 scientific papers (total in 4 papers)

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

A. N. Khisamiev

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

Abstract: We construct a family of $\Sigma$-uniform Abelian groups and a family of $\Sigma$-uniform rings. Conditions are specified that are necessary and sufficient for a universal $\Sigma$-function to exist in a hereditarily finite admissible set over structures in these families. It is proved that there is a set $S$ of primes such that no universal $\Sigma$-function exists in hereditarily finite admissible sets $\mathbb{HF}(G)$ and $\mathbb{HF}(K)$, where $G=\oplusŻ_p\mid p\in S\}$ is a group, $Z_p$ is a cyclic group of order $p$, $K=\oplus\{F_p\mid p\in S\}$ is a ring, and $F_p$ is a prime field of characteristic $p$.

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

Full text: PDF file (242 kB)
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English version:
Algebra and Logic, 2012, 51:1, 89–102

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. II”, Algebra Logika, 51:1 (2012), 129–147; Algebra and Logic, 51:1 (2012), 89–102

Citation in format AMSBIB
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\by A.~N.~Khisamiev
\paper $\Sigma$-uniform structures and $\Sigma$-functions.~II
\jour Algebra Logika
\yr 2012
\vol 51
\issue 1
\pages 129--147
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2986467}
\zmath{https://zbmath.org/?q=an:06115025}
\transl
\jour Algebra and Logic
\yr 2012
\vol 51
\issue 1
\pages 89--102
\crossref{https://doi.org/10.1007/s10469-012-9172-y}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84861895833}


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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. 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
    2. A. N. Khisamiev, “Universal functions over trees”, Algebra and Logic, 54:2 (2015), 188–193  mathnet  crossref  crossref  mathscinet  isi
    3. A. N. Khisamiev, “A class of almost $c$-simple rings”, Siberian Math. J., 56:6 (2015), 1133–1141  mathnet  crossref  crossref  mathscinet  isi  elib
    4. 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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