  For ease of exposition we shall make three simplifying assumptions concerning the theories under consideration.  First, we shall assume that all of our theories are couched in the language of set theory. There is no loss of generality in this assumption since every theory is mutually interpretable with a theory in this language.  For example, as noted earlier, PA and ZFC-Infinity are mutually interpretable.  Second, we shall assume that all of our theories contain ZFC-Infinity.  Third, we shall assume that all of our theories are Σ01-sound.