A metric version of Schlichting's Theorem

Une version métrique du théorème de Schlichting

Itaï Ben Yaacov (1) , Frank Olaf Wagner (1)

1 AGL - Algèbre, géométrie, logique

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

Mots clés: Schlichting's Theorem; invariant; metric structure; commensurable

Domaines: Logique [math.LO]; Théorie des groupes [math.GR]

Itaï Ben Yaacov, Frank Olaf Wagner. A metric version of Schlichting's Theorem. The Journal of Symbolic Logic, 2020, 85 (4), pp.1607-1613,. ⟨10.1017/jsl.2020.29⟩. ⟨hal-01523644v3⟩