Generic Theories for Series of Finite Abelian Groups

Generic Theories for Series of Finite Abelian Groups

The notion of a generic theory GTh( K , μ ) with respect to a measure μ was introduced in [Algebra and Logic, 53, No. 6, 512-519 (2014)]. Here, generic theories for two series of cyclic groups are described based on elementary invariants for Abelian groups and using a measure generated by a Frechet...

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Veröffentlicht in:Algebra and logic 2015, Vol.53 (6), p.471-480
Hauptverfasser: Mishchenko, A. A., Remeslennikov, V. N., Treier, A. V.
Format: Artikel
Sprache:eng
Schlagworte:
Abelian groups
Algebra
Finite groups
Mathematical Logic and Foundations
Mathematical research
Mathematics
Mathematics and Statistics
Series (Mathematics)
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Zusammenfassung:The notion of a generic theory GTh( K , μ ) with respect to a measure μ was introduced in [Algebra and Logic, 53, No. 6, 512-519 (2014)]. Here, generic theories for two series of cyclic groups are described based on elementary invariants for Abelian groups and using a measure generated by a Frechet filter. Axioms of generic theories are given, complete theories are characterized in terms of elementary invariants, and canonical models of complete theories are constructed.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-015-9309-x