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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

REFERENCES

Ahlbrandt, Gisela and Ziegler, Martin, Quasi-finitely axiomatizable totally categorical theories, Annals of Pure and Applied Logic, vol. 30 (1986), no.1, pp. 63–82, Stability in model theory (Trento, 1984).CrossRefGoogle Scholar
Ben Yaacov, Itaï, Berenstein, Alexander, Ward Henson, C., and Usvyatsov, Alexander, Model theory for metric structures, Model theory with Applications to Algebra and Analysis (Chatzidakis, Zoé, Macpherson, Dugald, Pillay, Anand, and Wilkie, Alex, editors), vol. 2, London Mathematical Society Lecture Note Series, vol. 350, Cambridge University Press, 2008, pp. 315–427.CrossRefGoogle Scholar
Ben Yaacov, Itaï, Berenstein, Alexander, and Melleray, Julien, Polish topometric groups, Transactions of the American Mathematical Society, vol. 365 (2013), no. 7, pp. 3877–3897.CrossRefGoogle Scholar
Ben Yaacov, Itaï, Definability of groups in ℵ 0-stable metric structures, this Journal vol. 75 (2010), no. 3, pp. 817–840.Google Scholar
Ben Yaacov, Itaï and Usvyatsov, Alexander, On d-finiteness in continuous structures, Fundamenta Mathematicae, vol. 194 (2007), pp. 67–88.CrossRefGoogle Scholar
Ben Yaacov, Itaï, Continuous first order logic and local stability, Transactions of the American Mathematical Society, vol. 362 (2010), no. 10, pp. 5213–5259.CrossRefGoogle Scholar
Effros, Edward G., Transformation groups and C*-algebras, Annals of Mathematics, Second Series, vol. 81 (1965), pp. 38–55.CrossRefGoogle Scholar
Kechris, Alexander S., Classical Descriptive Set Theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995.Google Scholar
Kuratowski, Kazimierz, Applications of the Baire-category method to the problem of independent sets, Fundamenta Mathematicae, vol. 81 (1973), no. 1, pp. 65–72.CrossRefGoogle Scholar
Malicki, Maciej, The automorphism group of the Lebesgue measure has no non-trivial subgroups of index <2ɷ, Colloquium Mathematicum, vol. 133 (2013), no. 2, pp. 169–174.CrossRefGoogle Scholar
Sabok, Marcin, Automatic continuity for isometry groups, preprint, arXiv:1312.5141.Google Scholar
Tsankov, Todor, Automatic continuity for the unitary group, Proceedings of the American Mathematical Society, vol. 141 (2013), no. 10, pp. 3673–3680.CrossRefGoogle Scholar