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      Infinitary Axiomatizability of Slender and Cotorsion-Free Groups

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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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          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

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              Classification of first order theories which have a structure theorem

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                Author and article information

                Journal
                28 October 1999
                Article
                math/9910162
                Custom metadata
                20A15 (Primary) 03C55, 03C75, 20A05, 20K20 (Secondary)
                Shelah [KlSh:709]
                math.LO

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