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GREY SUBSETS OF POLISH SPACES

Published online by Cambridge University Press:  22 December 2015

ITAÏ BEN YAACOV  and
JULIEN MELLERAY
ITAÏ BEN YAACOV
Affiliation:
UNIVERSITÉ CLAUDE BERNARD – LYON 1 INSTITUT CAMILLE JORDAN, CNRS UMR 5208 43 BOULEVARD DU 11 NOVEMBRE 1918 69622 VILLEURBANNE CEDEXFRANCE, URL: http://math.univ-lyon1.fr/∼begnac/URL: http://math.univ-lyon1.fr/∼melleray/
JULIEN MELLERAY
Affiliation:
UNIVERSITÉ CLAUDE BERNARD – LYON 1 INSTITUT CAMILLE JORDAN, CNRS UMR 5208 43 BOULEVARD DU 11 NOVEMBRE 1918 69622 VILLEURBANNE CEDEXFRANCE, URL: http://math.univ-lyon1.fr/∼begnac/URL: http://math.univ-lyon1.fr/∼melleray/
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Abstract

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.

Keywords

22A0503E15topometric groupgrey subsetgrey subgroupsmall index propertysmall density property
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 4 , December 2015 , pp. 1379 - 1397
Copyright
Copyright © The Association for Symbolic Logic 2015 

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References

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