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We say that a complete theory T has the Schröder-Bernstein property, or simply, the SB-property, if any two models M and N of T that are elementary bi-embeddable are isomorphic. The purpose of this talk is to study the SB-property for metric theories such as Hilbert spaces, probability algebras and expansions of these. Additionally, we will try to understand how the SB-property behaves under Randomizations, which is a natural way of mapping discrete first order structures to metric structures in a continuous language. This is joint work with Alexander Berenstein and Camilo Argoty presented in [1].
Reference
[1] Argoty, C., Berenstein, A. & Cuervo Ovalle, N. The SB-property on metric structures. Arch. Math. Logic (2025). https://doi.org/10.1007/s00153-024-00949-y