  To begin with, there is a useful characterization of the relation ≤.  Let us write T1 ⊆ Π01 T2 to indicate that every Π01-statement provable in T1 is also provable in T2.  A central result in the theory of interpretability is that (granting our simplifying assumptions) T1≤ T2 iff T1 ⊆ Π01 T2. It follows from this characterization and the second incompleteness theorem that for any theory T the theory T + Con(T) is strictly stronger than T, that is,   T &lt; T + Con(T).  Moreover, it follows from the arithmetized completeness theorem that the theory T + ¬Con(T) is interpretable in T, hence, T ≡ T + ¬Con(T).