理论的相对一致性

A Theory's Relative Consistency

证明理论的一致性有两种基本方法:一是直接给出满足理论的语义结构;二是从一种理论的一致性得到要证理论的一致性。相对化的方法属于第二种方法,它可以从弱系统的一致性证明强系统的一致性。相对化证明理论的一致性实质上是以某个理论为中介,间接地给出满足理论T的语义结构。相对化的本质是"保守性"的翻译,而"保守性"翻译恰是从弱系统证明强系统的关键。

Consistency is a basic requirement of a ＂good＂ theory.There are two basic methods to prove that a theory is consistent.One is to give a semantic structure which satisfies the theory and the other is to prove the consistency of the theory from the consistency of another theory.Relativisation is the method to prove a theory＇s consistency which belongs to the latter.It can prove a stronger theory＇s consistency from a weaker theory＇s consistency.It is shown that relativisation is essentially to give a theory T＇s semantic structure indirectly by a media—another theory which can describe the structure of the language of the theory T.The essence of relativization is a conservative translation,which is the key to prove the consistency of a stronger theory from that of the weaker.