The Schr\"oder-Bernstein property for weakly minimal theories
Logic
2009-12-09 v1
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.
Cite
@article{arxiv.0912.1363,
title = {The Schr\"oder-Bernstein property for weakly minimal theories},
author = {John Goodrick and Michael C. Laskowski},
journal= {arXiv preprint arXiv:0912.1363},
year = {2009}
}
Comments
17 pages; submitted