  The large cardinal axioms discussed above are naturally well-ordered in terms of strength.[11] This provides a natural way of climbing the hierarchy of interpretability.  At the base we start with the theory ZFC-Infinity and then we climb to ZFC and up through ZFC+Φ for various large cardinal axioms Φ.  Notice that for two large cardinal axioms Φ and Ψ, if Ψ is stronger than Φ then Ψ implies that there is a standard model of Φ and so we have a natural interpretation of ZFC+Φ in ZFC+Ψ.