图灵级数的逻辑
The logic of Turing progressions
摘要：
图灵级数通过迭代地将一致性声明添加到基础理论中而产生。不同的一致性概念会产生不同的图灵级数。在本文中，我们提出了一个逻辑，产生正是所有的关系，这些不同的图灵级数之间的一组特定的自然一致性概念。因此，所提出的逻辑被证明是算术的声音和完整的自然解释，命名为\emph{Formalized Turing progressions}（FTP）的解释。
英文摘要：
Turing progressions arise by iteratedly adding consistency statements to a base theory. Different notions of consistency give rise to different Turing progressions. In this paper we present a logic that generates exactly all relations that hold between these different Turing progressions given a particular set of natural consistency notions. Thus, the presented logic is proven to arithmetically sound and complete for a natural interpretation, named the \emph{Formalized Turing progressions} (FTP) interpretation.
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