The Schröder-Bernstein property for weakly minimal theories

Details The Schröder-Bernstein property for weakly minimal theories The Schröder-Bernstein property for weakly minimal theories

2009-12-07

arxiv.org/abs/0912.1363v1

Mathematics

Logic

17 pages; submitted

Scientific paper

For a countable, weakly minimal theory, we show that the Schroeder-Bernstein property (any two elementarily bi-embeddable models are isomorphic) is equivalent to both a condition on orbits of rank 1 types and the property that the theory has no infinite collection of pairwise bi-embeddable, pairwise nonisomorphic models. We conclude that for countable weakly minimal theories, the Schroeder-Bernstein property is absolute between transitive models of ZFC.

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