Abstract: 

We say that a complete theory T has the Schröder-Bernstein property, or simply the SB-property, if for any two models M and N of T that are elementary bi-embeddable then they are isomorphic. The purpose of this talk is to study the SB-property for stable metric theories such as probability algebras and Randomizations, which is a natural way of mapping discrete first order structures to metric structures in a continuous language.

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