The Schroder-Bernstein property for theories of abelian groups
Abstract
Description
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/H^0) is unipotent.
17 pages
17 pages