Divisible rigid groups. II: Stability, saturation, and elementary submodels

DOI10.1007/s10469-018-9476-7zbMath1485.03126OpenAlexW2803258312MaRDI QIDQ1792003

N. S. Romanovskii, Alexei G. Myasnikov

Publication date: 11 October 2018

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10469-018-9476-7

zbMATH Keywords

stabilitysaturationtheorymodeldivisible rigid group\(\forall\exists\)-formula

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Other classes of groups defined by subgroup chains (20F22) Derived series, central series, and generalizations for groups (20F14) Classification theory, stability, and related concepts in model theory (03C45) Models with special properties (saturated, rigid, etc.) (03C50) Quantifier elimination, model completeness, and related topics (03C10)

Related Items (8)

Generalized rigid groups: definitions, basic properties, and problems ⋮ Divisible rigid groups. Morley rank ⋮ Equational Noethericity of metabelian \(r\)-groups ⋮ Generic types and generic elements in divisible rigid groups ⋮ Divisible rigid groups. IV: Definable subgroups ⋮ Generalized rigid metabelian groups ⋮ Divisible rigid groups. III: Homogeneity and quantifier elimination ⋮ Two facts on model theory for divisible rigid groups

Cites Work

• Divisible rigid groups.
• Krull dimension of solvable groups.
• Universal theories for rigid soluble groups.
• Divisible rigid groups. Algebraic closedness and elementary theory

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