Continuous first order logic for unbounded metric structures
- ITAÏ BEN YAACOV, BEN YAACOV
We develop Fraïssé theory, namely the theory of Fraïssé classes and Fraïssé limits, in the context of metric structures. We show that a class of finitely generated structures is Fraïssé if and only if it is the age of a separable approximately homogeneous structure, and conversely, that this structure is necessarily the unique limit of the class, and is universal for it. We do this in a somewhat new approach, in which “finite maps up to errors” are coded by approximate isometries.