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FRAÏSSÉ LIMITS OF METRIC STRUCTURES

Published online by Cambridge University Press:  13 March 2015

ITAÏ BEN YAACOV
ITAÏ BEN YAACOV*
Affiliation:
UNIVERSITÉ CLAUDE BERNARD – LYON 1, INSTITUT CAMILLE JORDAN, CNRS UMR 5208, 43 BOULEVARD DU 11 NOVEMBRE 1918, 69622 VILLEURBANNE CEDEX, FRANCEURL: http://math.univ-lyon1.fr/∼begnac/
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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.

Keywords

03C30,03C52Fraïssé classFraïssé limitmetric structureultrahomogeneous structureapproximate isometryKatětov functionGurarij space
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 1 , March 2015 , pp. 100 - 115
Copyright
Copyright © The Association for Symbolic Logic 2015 

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References

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