2007/05/13 by John Goodrick, Goodrick, John
Mathematics · #03C45 (Primary) 03C52 #20K99 (Secondary) #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras #math.GR #math.LO #msc:03C45 #msc:03C52 #msc:20K99
paper · pdf · doi:10.48550/arxiv.0705.1850
17 pages
arxiv created 2007/05/13 · openalex publication_date 2007/05/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A first-order theory has the Schroder-Bernstein property if any two of its models that are elementarily bi-embeddable are isomorphic. We prove that if G is an abelian group, then the follwing are equivalent: 1. Th(G, +) has the Schroder-Bernstein property; 2. Th(G, +) is omega-stable; 3. G is the direct sum of a divisible group and a torsion group of bounded exponent; 4. Th(G, +) is superstable, and if (H, +) is a saturated elementary extension of (G,+), every map in Aut(H/H0) is unipotent.