FRAÏSSÉ LIMITS OF METRIC STRUCTURES

Abstract

Abstract 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 .