 Suppose T1 and T2 are recursively enumerable axiom systems. We say that T1 is interpretable in T2 (T1 ≤ T2) when, roughly speaking, there is a translation τ from the language of T1 to the language of T2 such that, for each sentence ϕ of the language of T1, if T1 ⊢ ϕ then T2 ⊢ τ(ϕ). We shall write T1 &lt; T2 when T1 ≤ T2 and T2 ≰ T1 and we shall write T1 ≡ T2 when both T1 ≤ T2 and T2 ≤ T1. In the latter case, T1 and T2 are said to be mutually interpretable. The equivalence class of all theories mutually interpretable with T is called the interpretability degree of T. The interpretability hierarchy is the collection of all theories ordered under the relation ≤. 