Divisible Rigid Groups. II. Stability, Saturation, and Elementary Submodels

A. G. Myasnikov, N. S. Romanovskii

Результат исследования: Научные публикации в периодических изданияхстатья

3 Цитирования (Scopus)

Аннотация

A group G is said to be rigid if it contains a normal series G = G1 > G2 > . . . > Gm > Gm+1 = 1, whose quotients Gi/Gi+1 are Abelian and, treated as right ℤ[G/Gi]- modules, are torsion-free. A rigid group G is divisible if elements of the quotient Gi/Gi+1 are divisible by nonzero elements of the ring ℤ[G/Gi]. Every rigid group is embedded in a divisible one. Previously, it was stated that the theory Im of divisible m-rigid groups is complete. Here, it is proved that this theory is ω-stable. Furthermore, we describe saturated models, study elementary submodels of an arbitrary model, and find a representation for a countable saturated model in the form of a limit group in the Fraïssé system of all finitely generated m-rigid groups. Also, it is proved that the theory Im admits quantifier elimination down to a Boolean combination of ∀∃-formulas.

Язык оригиналаанглийский
Страницы (с-по)29-38
Число страниц10
ЖурналAlgebra and Logic
Том57
Номер выпуска1
DOI
СостояниеОпубликовано - 1 мая 2018

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