 Roughly, a theory \(T_1\) is interpretable in another theory \(T_2\) if the primitive concepts and the range of the variables of \(T_1\) are definable in \(T_2\) so that it is possible to translate every theorem of \(T_1\) into a theorem of \(T_2\). One should not misunderstand such interpretations as providing anything like intuitive synonymity. Two theories may have radically different intended subject matter and yet, as formal systems, one may be interpretable in another. (As an illustration: a simple theory of ancestors may be, taken as a formal system, interpreted in arithmetic; obviously this does not mean that grandmothers and such are really numbers.) What is significant is that interpretability preserves certain elementary formal properties of theories, most importantly, consistency: if \(T_1\) is interpretable in \(T_2\) and \(T_2\) is consistent, \(T_1\) is also consistent. And any system in which Q can be interpreted is guaranteed to be essentially incomplete. For any such theory in which Q is interpretable, the incompleteness could be proved also directly; for example, in various theories of set theory, one can code formulas and derivations (instead of numbers) by sets, “Gödel sets”, and proceed then as usual (see, e.g., Fitting 2007). However, for most purposes, it is just much simpler to establish the interpretability of Q in the theory at issue.