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Algebra Logika, 2014, Volume 53, Number 6, Pages 722–734 (Mi al663)  

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

Generic theories for series of finite Abelian groups

A. A. Mishchenkoab, V. N. Remeslennikova, A. V. Treierab

a Omsk Branch of Sobolev Institute of Mathematics, ul. Pevtsova 13, Omsk, 644099, Russia
b Omsk State Technical University, pr. Mira 11, Omsk, 644050, Russia

Abstract: The notion of a generic theory $\mathsf{GTh}(\mathcal K,\mu)$ with respect to a measure $\mu$ was introduced in [Algebra i Logika, 53, No. 6, 779–789 (2014)]. Here, based on elementary invariants for Abelian groups and using a measure generated by a Frechet filter, we describe generic theories for two series of cyclic groups. Axioms of generic theories are given, complete theories are characterized in terms of elementary invariants, and canonical models of complete theories are constructed.

Keywords: generic theory with respect to measure, Frechet filter, finite Abelian group.

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English version:
Algebra and Logic, 2015, 53:6, 471–480

Bibliographic databases:

UDC: 512.541+512.54.01
Received: 26.11.2014

Citation: A. A. Mishchenko, V. N. Remeslennikov, A. V. Treier, “Generic theories for series of finite Abelian groups”, Algebra Logika, 53:6 (2014), 722–734; Algebra and Logic, 53:6 (2015), 471–480

Citation in format AMSBIB
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\by A.~A.~Mishchenko, V.~N.~Remeslennikov, A.~V.~Treier
\paper Generic theories for series of finite Abelian groups
\jour Algebra Logika
\yr 2014
\vol 53
\issue 6
\pages 722--734
\mathnet{http://mi.mathnet.ru/al663}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3408306}
\transl
\jour Algebra and Logic
\yr 2015
\vol 53
\issue 6
\pages 471--480
\crossref{https://doi.org/10.1007/s10469-015-9309-x}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84924120351}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Myasnikov, V. N. Remeslennikov, “Generic theories as a method for approximating elementary theories”, Algebra and Logic, 53:6 (2015), 512–519  mathnet  crossref  mathscinet  isi
  • Алгебра и логика Algebra and Logic
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