理论的相对一致性

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。

A Theory's Relative Consistency

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 ...