 Of course, there are many important and interesting theories in mathematics which are not even formulated in the language of arithmetic. However, the applicability of the incompleteness theorems can be dramatically extended outside the language of first-order arithmetic and its extensions, when it is noted that all that is needed is that weak theories such as Q, or PRA, can be interpreted in the system in question. Most importantly, this involves various systems of set theory. For example, the incompleteness theorems hold for ZFC–Inf (i.e., ZFC without the axiom of infinity) and all its extensions, however strong (as long as they are axiomatizable.)