The Schroder-Bernstein property for a-saturated models
Logic
2012-04-17 v2
Abstract
A first-order theory T has the Schr\"oder-Bernstein (SB) property if any pair of elementarily bi-embeddable models are isomorphic. We prove that T has an expansion by constants that has the SB property if and only if T is superstable and non-multidimensional. We also prove that among superstable theories T, the class of a-saturated models of T has the SB property if and only if T has no nomadic types.
Cite
@article{arxiv.1202.6535,
title = {The Schroder-Bernstein property for a-saturated models},
author = {John Goodrick and Michael C. Laskowski},
journal= {arXiv preprint arXiv:1202.6535},
year = {2012}
}
Comments
13 pages