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Infinitary Axiomatizability of Slender and Cotorsion-Free Groups
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28 October 1999
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Abstract
The classes of slender and cotorsion-free abelian groups are axiomatizable in the infinitary logics L_{infty,omega_1} and L_{infty,omega}, respectively. The Baer-Specker group Z^omega is not L_{infty,omega_1}-equivalent to a slender group.
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Most cited references3
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Abelian groups without elements of finite order
Reinhold Baer (1937)
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Existence of many L∞,λ-equivalent, non- isomorphic models of T of power λ
Saharon Shelah (1987)
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Classification of first order theories which have a structure theorem
Saharon Shelah (1985)