Divisible Rigid Groups. II. Stability, Saturation, and Elementary Submodels Full article
| Journal |
Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302 |
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| Output data | Year: 2018, Volume: 57, Number: 1, Pages: 29-38 Pages count : 10 DOI: 10.1007/s10469-018-9476-7 | ||||||
| Tags | divisible rigid group; model; saturation; stability; theory; ∀∃-formula | ||||||
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Abstract:
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.
Cite:
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
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
Identifiers:
| Web of science: | WOS:000433237600003 |
| Scopus: | 2-s2.0-85047136866 |
| OpenAlex: | W2803258312 |