度量结构的Fraïssé极限

摘要：

在度量结构的背景下，我们发展了\emph{Fraïssé theory}，即\emph{Fraïssé classes}和\emph{Fraïssé limits}的理论。我们证明了一类可分的近似齐次结构是Fraïssé当且仅当它是可分的近似齐次结构的年龄，并且相反，这个结构必然是该类的唯一极限，并且对它是泛的。我们用一种新的方法来做这件事，其中“有限映射到错误”是由\emph{approximate isometries}编码的。

英文摘要：

We develop \emph{Fraïssé theory}, namely the theory of \emph{Fraïssé classes} and \emph{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 \emph{approximate isometries}.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。