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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

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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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