  This paper deals with three tools to compare proof-theoretic strength of
formal arithmetical theories: interpretability, $\Pi^0_1$-conservativity and
proving restricted consistency. It is well known that under certain conditions
these three notions are equivalent and this equivalence is often referred to as
the Orey-H\'ajek characterization of interpretability.
  In this paper we look with detail at the Orey-H\'ajek characterization and
study what conditions are needed and in what meta-theory the characterizations
can be formalized.
