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.

We generalize two concepts from special cases of Polish group actions to the general case. The two concepts are elementary embeddability, from model theory, and analytic sets, from the usual descriptive set theory.

We present a framework for model theoretic forcing in a non first order context, and present some applications of this framework to Banach space theory.