G{\"o}del's second incompleteness theorem forbids to prove, in a given theory U, the consistency of many theories-in particular, of the theory U itself-as well as it forbids to prove the normalization property for these theories, since this property implies their consistency. When we cannot prove in a theory U the consistency of a theory T , we can try to prove a relative consistency theorem, that is, a theorem of the form: If U is consistent then T is consistent. Following the same spirit, we show in this paper how to prove relative normalization theorems, that is, theorems of the form: If U is 1-consistent, then T has the normalization property.

翻译：哥德尔第二不完备定理禁止在给定理论U中证明许多理论——特别是理论U本身——的一致性，同时也禁止证明这些理论的归一化性质，因为该性质蕴含其一致性。当我们无法在理论U中证明理论T的一致性时，可以尝试证明相对一致性定理，即形如“若U一致则T一致”的定理。遵循相同思路，本文展示了如何证明相对归一化定理，即形如“若U是1-一致的，则T具有归一化性质”的定理。