Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T17:32:55.380Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Hjorth's oscillation theorem

Published online by Cambridge University Press:  12 March 2014

Julien Melleray
Julien Melleray*
Affiliation:
Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan, 43 Blvd Du 11 Novembre 1918, F-69622 Villeurbanne-Cedex, France. E-mail: melleray@math.univ-lyonl.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

We reformulate, in the context of continuous logic, an oscillation theorem proved by G. Hjorth and give a proof of the theorem in that setting which is similar to, but simpler than, Hjorth's original one. The point of view presented here clarifies the relation between Hjorth's theorem and first-order logic.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 4 , December 2010 , pp. 1359 - 1365
Copyright
Copyright © Association for Symbolic Logic 2010

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]Yaacov, Itaï Ben, Berenstein, Alexander, Henson, C. Ward, and Usvyatsov, Alexander, Model theory for metric structures, (Chatzidakis, Zoé, MacPherson, Dugald, Pillay, Anand, and Wilkie, Alex, editors), London Mathematical Society Lecture Note Series, vol. 350, 2008, pp. 315–427.Google Scholar
[2]Gao, Su, Invariant descriptive set theory. Pure and Applied Mathematics, CRC Press, Boca Raton, FL, 2009.Google Scholar
[3]Hjorth, Greg, An oscillation theorem for groups of isometries, Geometry and Functional Analysis, vol. 18 (2008), no. 2, pp. 489–521.CrossRefGoogle Scholar
[4]Pestov, Vladimir, Dynamics of infinite-dimensional groups and Ramsey-type phenomena, Publicações dos Colóquios de Matemática, IMPA, Rio de Janeiro, 2005.Google Scholar