组合真值模型的局部集合方案和端扩张
Local collection scheme and end-extensions of models of compositional truth
摘要：
我们介绍了一个原则的组成真谓词的本地收集，并表明它是保守的经典组成理论的真理在算术设置。这条公理指出，在限制到任何语法复杂度的公式时，所得到的谓词满足完全集合。特别是，使用集合的真值谓词应用于任何给定（代码）证明中出现的句子的论点不足以表明该证明的结论是真的，这与归纳方案的情况形成鲜明对比。我们分析了各种进一步的结果有关的最终扩展模型的组成的真理和收集计划的组成的真理谓词。
英文摘要：
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.
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