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A METRIC VERSION OF SCHLICHTING’S THEOREM

Published online by Cambridge University Press:  07 September 2020

ITAÏ BEN YAACOV
Affiliation:
UNIVERSITÉ DE LYON, CNRS UNIVERSITÉ CLAUDE BERNARD LYON 1 INSTITUT CAMILLE JORDAN UMR5208 43 BD DU 11 NOVEMBRE 1918 69622 VILLEURBANNE CEDEX, FRANCE E-mail: benyaacov@math.univ-lyon1.fr E-mail: wagner@math.univ-lyon1.fr URL: http://math.univ-lyon1.fr/~wagner/ URL: http://math.univ-lyon1.fr/~begnac/
FRANK O. WAGNER
Affiliation:
UNIVERSITÉ DE LYON, CNRS UNIVERSITÉ CLAUDE BERNARD LYON 1 INSTITUT CAMILLE JORDAN UMR5208 43 BD DU 11 NOVEMBRE 1918 69622 VILLEURBANNE CEDEX, FRANCE E-mail: benyaacov@math.univ-lyon1.fr E-mail: wagner@math.univ-lyon1.fr URL: http://math.univ-lyon1.fr/~wagner/ URL: http://math.univ-lyon1.fr/~begnac/

Abstract

If ${\mathfrak {F}}$ is a type-definable family of commensurable subsets, subgroups or subvector spaces in a metric structure, then there is an invariant subset, subgroup or subvector space commensurable with ${\mathfrak {F}}$. This in particular applies to type-definable or hyper-definable objects in a classical first-order structure.

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© The Association for Symbolic Logic 2020

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References

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