2012/03/20 by Itaï Ben Yaacov, Yaacov, Itaï Ben
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.1203.4459
arxiv created 2014/09/08 · arxiv updated 2014/09/09
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.