Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T21:23:23.135Z Has data issue: false hasContentIssue false
  • English
  • Français

The complexity of squares in the group of isometries of the Baire space

Published online by Cambridge University Press:  12 March 2014

Aaron Hill
Aaron Hill*
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign,1409 W. Green St., Urbana, Il 61801, USA, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that in the Polish group of isometries of the Baire space the collection of n-th powers is non-Borel. We also prove that in the Polish space of trees on ℕ the collection of trees that have an automorphism under which every node has order exactly n is non-Borel.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 1 , March 2012 , pp. 329 - 336
Copyright
Copyright © Association for Symbolic Logic 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Ageev, O., The generic automorphism of a Lebesgue space is conjugate to a G-extension for any finite abelian group G, Doklady. Mathematics, vol. 62 (2000), pp. 216–219.Google Scholar
[2]Gartside, P. and Pejić, B., The complexity of the set of squares in the homeomorphism group of the circle, Fundamenta Mathematicae, vol. 195 (2007), pp. 125–134.CrossRefGoogle Scholar
[3]Halmos, P. R., Lectures on ergodic theory, Chelsea Publishing Company, 1956.Google Scholar
[4]Humke, P. and Laczkovich, M., The Borel structure of iterates of continuous functions, Proceedings of the Edinburgh Mathematical Society, vol. 32 (1989), pp. 483–494.CrossRefGoogle Scholar
[5]Kechris, A., Classical descriptive set theory, Springer-Verlag, 1995.CrossRefGoogle Scholar
[6]King, J., The generic transformation has roots of all orders, Colloquium Mathematicum, vol. 84–85 (2000), pp. 521–547.CrossRefGoogle Scholar
[7]de Sam Lazaro, J. and de La Rue, T., Une transformation générique peut être insérée dans un flot, Annales de l'Institut Henri Poincaré. Probabilités et Statistiques, vol. 39 (2003), pp. 121–134.Google Scholar