The Schroder-Bernstein property for a-saturated models

Details The Schroder-Bernstein property for a-saturated models The Schroder-Bernstein property for a-saturated models

2012-02-29

arxiv.org/abs/1202.6535v2

Mathematics

Logic

13 pages

Scientific paper

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.

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