Divisible Rigid Groups. II. Stability, Saturation, and Elementary Submodels | Sciact - Система учета научной деятельности ИМ СО РАН

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

Журнал

Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302

Вых. Данные

Год: 2018, Том: 57, Номер: 1, Страницы: 29-38 Страниц : 10 DOI: 10.1007/s10469-018-9476-7

Ключевые слова

divisible rigid group; model; saturation; stability; theory; ∀∃-formula

Авторы

Myasnikov A.G. ¹ , Romanovskii N.S. ^2,3

Организации

1	Schaefer School of Engineering and Science, Department of Mathematical Sciences, Stevens Institute of Technology, Castle Point on Hudson, Hoboken, NJ 07030-5991, United States
2	Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russian Federation
3	Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russian Federation

A group G is said to be rigid if it contains a normal series G = G1G2GmGm+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 m 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 m admits quantifier elimination down to a Boolean combination of ∀∃-formulas. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Myasnikov A.G. , Romanovskii N.S.
Divisible Rigid Groups. II. Stability, Saturation, and Elementary Submodels
Algebra and Logic. 2018. V.57. N1. P.29-38. DOI: 10.1007/s10469-018-9476-7 WOS Scopus OpenAlex

Web of science:	WOS:000433237600003
Scopus:	2-s2.0-85047136866
OpenAlex:	W2803258312

БД	Цитирований
Scopus	10
OpenAlex	9
Web of science	9