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- W2969354420 abstract "We study limit models in the class of abelian groups with the subgroup relation and in the class of torsion-free abelian groups with the pure subgroup relation. We show: Theorem 0.1(1)If G is a limit model of cardinality λ in the class of abelian groups with the subgroup relation, then G≅(⊕λQ)⊕⊕pprime(⊕λZ(p∞)).(2)If G is a limit model of cardinality λ in the class of torsion-free abelian groups with the pure subgroup relation, then:•If the length of the chain has uncountable cofinality, thenG≅(⊕λQ)⊕Πpprime(⊕λZ(p))‾.•If the length of the chain has countable cofinality, then G is not algebraically compact. Theorem 0.1 If G is a limit model of cardinality λ in the class of abelian groups with the subgroup relation, then G≅(⊕λQ)⊕⊕pprime(⊕λZ(p∞)). If G is a limit model of cardinality λ in the class of torsion-free abelian groups with the pure subgroup relation, then: If the length of the chain has uncountable cofinality, thenG≅(⊕λQ)⊕Πpprime(⊕λZ(p))‾. If the length of the chain has countable cofinality, then G is not algebraically compact." @default.
- W2969354420 created "2019-08-29" @default.
- W2969354420 creator A5065698017 @default.
- W2969354420 date "2020-01-01" @default.
- W2969354420 modified "2023-10-03" @default.
- W2969354420 title "Algebraic description of limit models in classes of abelian groups" @default.
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- W2969354420 doi "https://doi.org/10.1016/j.apal.2019.102723" @default.
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