 Observe that the satisfaction of Conservativeness and Eliminability criteria, whether in their semantic or their syntactic formulation, is not an absolute property of a definition; the satisfaction is relative to the ground language. Different ground languages can have associated with them different systems of proof and different classes of interpretations. Hence, a definition may satisfy the two criteria when added to one language, but may fail to do so when added to a different language. For further discussion of the criteria, see Suppes 1957 and Belnap 1993.