The Schröder-Bernstein Property for Theories of Abelian Groups
نویسنده
چکیده
A first-order theory has the Schröder-Bernstein Property if any two of its models that are elementarily bi-embeddable are isomorphic. We prove (as Theorem 3.8): Theorem 1. If G is an abelian group, then the following are equivalent: 1. Th(G,+) has the Schröder-Bernstein property; 2. Th(G,+) is ω-stable; 3. G is the direct sum of a divisible group and a torsion group of
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