Grey subsets of Polish spaces

Itaï Ben Yaacov (1) , Julien Melleray (1)

1 AGL - Algèbre, géométrie, logique

We develop the basics of an analogue of descriptive set theory for functions on a Polish space $X$. We use this to define a version of the small index property in the context of Polish topometric groups, and show that Polish topometric groups with ample generics have this property. We also extend classical theorems of Effros and Hausdorff to the topometric context.

Mots clés: grey subset; topometric group; small index property; grey subgroup; small density property

Domaines: Logique [math.LO]

Itaï Ben Yaacov, Julien Melleray. Grey subsets of Polish spaces. 2014. ⟨hal-00576533v3⟩