算术一致性的均匀性与哥德尔第二不完备定理： Ein M"archen

在广受关注的工作中，Artemov 最近展示了对于 $\mathrm{PA}$，一致性模式虽然无法证明其对应的统一一致句子 $\mathrm{Con}(\mathrm{PA})$，却可通过选择器证明实现统一验证。 In this note, we recast that this phenomenon extends to all sufficiently strong arithmetizable theories: For such theories $T$, there exists a primitive recursive selector producing proofs of all instances of the associated consistency schema. This results -- a soft version of a classical result of Pudl\'ak -- yields a form of computational uniformity, despite the fact that it cannot be internalized as the uniform consistency sentence of G"odel's Second Incompleteness Theorem. Our main goal is to analyze this gap and to locate selector proofs within the broader framework of provability and reflection.