Separating Classes of Groups by First-Order Sentences

DOI10.1142/S0218196703001286zbMath1059.20002OpenAlexW2124807316MaRDI QIDQ3043615

André Nies

Publication date: 6 August 2004

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218196703001286

zbMATH Keywords

first-order logicfinitely generated groupsword problemfinitely presented groupsprime modelsclasses of groupsquasi finitely axiomatizable groups

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Model-theoretic algebra (03C60) Generators, relations, and presentations of groups (20F05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Quasivarieties and varieties of groups (20E10) Recursively (computably) enumerable sets and degrees (03D25) Axiomatics and elementary properties of groups (20A05)

Related Items (18)

First-order rigidity of rings satisfying polynomial identities ⋮ Comparing quasi-finitely axiomatizable and prime groups ⋮ Bi-interpretability and QFA structures: study of some soluble groups and commutative rings. (Bi-interprétabilité et structures QFA : étude de groupes résolubles et des anneaux commutatifs ⋮ R.J. THOMPSON’S GROUPSFANDTARE BI-INTERPRETABLE WITH THE RING OF THE INTEGERS ⋮ First order rigidity of non-uniform higher rank arithmetic groups ⋮ Polycyclic-by-finite groups and first-order sentences ⋮ Regular bi-interpretability of Chevalley groups over local rings ⋮ Defining \(R\) and \(G(R)\) ⋮ Bounded generation and commutator width of Chevalley groups: function case ⋮ On the model theory of higher rank arithmetic groups ⋮ Elementary equivalence of rings with finitely generated additive groups ⋮ Describing Groups ⋮ 2010 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '10 ⋮ Finitely generated groups are universal among finitely generated structures ⋮ Aspects of free groups. ⋮ Quasi-finitely axiomatizable nilpotent groups ⋮ Quasi-finitely axiomatizable groups and groups which are prime models ⋮ 2005 Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '05

Cites Work

• Undecidable fragments of elementary theories
• On a correspondence between rings and groups
• Commutators of Certain Finitely Generated Soluble Groups
• Unnamed Item

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