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.
"A note on Hjorth's oscillation theorem." J. Symbolic Logic 75 (4) 1359 - 1365, December 2010. https://doi.org/10.2178/jsl/1286198151