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Preprint Number 429
429. John Goodrick and Michael C. Laskowski
The Schröder-Bernstein property for a-saturated models
Submission date: 1 March 2012.
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.
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