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Preprint Number 222

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222. John Goodrick, Michael C. Laskowski
The Schröder-Bernstein property for weakly minimal theories
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Submission date: 7 December 2009.

Abstract:

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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