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Algebra i 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
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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.
Received: 26.11.2014
English version:
Algebra and Logic, 2015, Volume 53, Issue 6, Pages 471–480
DOI: https://doi.org/10.1007/s10469-015-9309-x
Bibliographic databases:
Document Type: Article
UDC: 512.541+512.54.01
Language: Russian
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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\paper Generic theories for series of finite Abelian groups
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\pages 722--734
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и логика Algebra and Logic
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