The Journal of Symbolic Logic

Research Article

A Note on Hjorth's oscillation theorem

Julien Melleray

Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan, 43 Blvd Du 11 Novembre 1918, F-69622 Villeurbanne-Cedex, France. E-mail:


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.

(Received June 29 2009)