English

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

R2 v1 2026-06-21T20:26:54.039Z