We formulate, within the frame-theory $Q$ for the foundations of Mathematics outlined in [2], a list $L$ of axioms which state that almost all "interesting" collections and almost all "interesting" operations are elements of the universe. The resulting theory $Q+L$ would thus have the important foundational feature of being completely self-contained. Unfortunately, the whole list $L$ is inconsistent, and we are led to formulate the following problem, which we call the problem of self-reference: "Find out maximal subsystems of $L$ relatively consistent with the frame-theory $Q$". No complete answer being available up to now, we leave the question to the attention of all interested mathematicians (for partial answers, see [3]).