Undecidable Lt theories of topological abelian groups

DOI10.2307/2273225zbMath0482.03016OpenAlexW2083405924MaRDI QIDQ3939789

Gregory L. Cherlin, Peter H. Schmitt

Publication date: 1981

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2273225

zbMATH Keywords

topological groupshereditary undecidabilitytopological model theoryfirst order theory of topological abelian groupsHausdorff topological abelian groupslocally pure Hausdorff topological abelian groupssaturated torsion-free locally pure topological abelian groupstorsion-free Hausdorff topological abelian groups

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Applications of logic to group theory (20A15) Model theory (03C99) Decidability of theories and sets of sentences (03B25) Torsion-free groups, infinite rank (20K20) Topological methods for abelian groups (20K45)

Related Items (2)

Stability theory for topological logic, with applications to topological modules ⋮ Locally pure topological Abelian groups: Elementary invariants

Cites Work

• Proof of a lemma on model completeness
• The theory of Abelian groups with predicates specifying a subgroup, and with endomorphism operations
• Theories of Abelian groups with predicates specifying a subgroup
• Elementary theory of abelian groups without trosion, with a predicate selecting a subgroup
• Sentences Preserved between Equivalent Topological Bases
• A language for topological structures which satisfies a Lindström-theorem
• Infinitary logic and topological homeomorphisms
• Model theory of topological structures
• Elementary properties of ordered abelian groups
• The elementary theory of abelian groups

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