Submission date: 1 March 2012.

Abstract:

A first-order theory T has the Schröder-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.

Mathematics Subject Classification: 03C45, 03C52

Keywords and phrases: Schröder-Bernstein, a-saturated, non-multidimensional, classification theory.

Full text arXiv 1202.6535: pdf, ps.