论文标题
本地收集计划和组成真理模型的最终范围
Local collection scheme and end-extensions of models of compositional truth
论文作者
论文摘要
我们介绍了一个本地收集原则，以构成真理谓词，并表明它在算术环境中对经典的真理理论是保守的。该公理指出，在限制任何句法复杂性的公式时，所得的谓词可以满足完整的收集。特别是，使用收集的参数用于真实的谓词，应用于任何给定的（A）证明的句子，不足以证明该证明的结论是真实的，与归纳方案的情况形成了鲜明的对比。我们分析了有关组成真理模型的最终延伸以及组成真理谓词的收集方案的各种进一步结果。
We introduce a principle of local collection for compositional truth predicates and show that it is conservative over the classically compositional theory of truth in the arithmetical setting. This axiom states that upon restriction to formulae of any syntactic complexity, the resulting predicate satisfies full collection. In particular, arguments using collection for the truth predicate applied to sentences occurring in any given (code of a) proof do not suffice to show that the conclusion of that proof is true, in stark contrast to the case of induction scheme. We analyse various further results concerning end-extensions of models of compositional truth and the collection scheme for the compositional truth predicate.
