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arXiv · 0912.1363

The Schröder-Bernstein property for weakly minimal theories

John Goodrick·Michael C. Laskowski
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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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John Goodrick, Michael C. Laskowski. 2009-12-07. The Schröder-Bernstein property for weakly minimal theories. https://arxiv.org/abs/0912.1363

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