  Product update is an operation on models introduced into epistemic logic in
order to represent a broad class of informational events. If adding modalities
representing product update to a language does not alter its expressive power
then we say that the language is "closed for product update." The basic modal
language is known to be closed for product update. We establish that monadic
second order logic is closed for product update (Theorem 5). Our technique is
to pass via an intermediate language with what we call "action nominals." We
obtain as corollaries that propositionally quantified modal logic is closed for
product update, as is the modal mu-calculus.
