When does elementary bi-embeddability imply isomorphism?
Logic
2007-05-23 v1
Abstract
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 a countable theory T has the Schroder-Bernstein property then it is classifiable (it is superstable and has NDOP and NOTOP) and satisfies a slightly stronger condition than nonmultidimensionality, namely: there cannot be a model M of T, a type p over M, and an automorphism f of M such that for every two distinct natural numbers i and j, f^i(p) is orthogonal to f^j(p). We also make some conjectures about how the class of theories with the Schroder-Bernstein property can be characterized.
Cite
@article{arxiv.0705.1849,
title = {When does elementary bi-embeddability imply isomorphism?},
author = {John Goodrick},
journal= {arXiv preprint arXiv:0705.1849},
year = {2007}
}