§ Joke Definition of Metatheorem

A metatheorem is a theorem that can become false when you add another axiom!

Recall that adding an axiom can never disprove previous theorems, since all previous theorems rely on existing axioms that are unchanged by the addition of a new theorem. In contrast, a metatheorem is a theorem about a formal system, and can become false if another axiom is added to the system, since e.g. some syntactic property of the axiom system may no longer hold (think: subformula property).