|
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.
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
Linking options:
https://www.mathnet.ru/eng/al663 https://www.mathnet.ru/eng/al/v53/i6/p722
|
Statistics & downloads: |
Abstract page: | 311 | Full-text PDF : | 69 | References: | 50 | First page: | 18 |
|