一个鲁棒的证明论良序
A robust proof-theoretic well-ordering
摘要：
众所周知，自然公理理论是由逻辑强度预良序的，根据逻辑强度的各种表征，如一致性强度和包含$Π^0_1$定理。虽然这些逻辑强度的概念与自然理论相一致，但它们并不是一般等价的。我们研究这些概念的类似物-如$Π^1_1$ -反射强度和包含$Π^1_1$定理-在存在$Σ^1_1$真理的神谕。在这种情况下，这些概念是一致的;此外，我们得到了公理化理论的真正的预良序，并可能放弃对“自然”理论的非数学量化。
英文摘要：
It is well-known that natural axiomatic theories are pre-well-ordered by logical strength, according to various characterizations of logical strength such as consistency strength and inclusion of $Π^0_1$ theorems. Though these notions of logical strength coincide for natural theories, they are not generally equivalent. We study analogues of these notions -- such as $Π^1_1$-reflection strength and inclusion of $Π^1_1$ theorems -- in the presence of an oracle for $Σ^1_1$ truths. In this context these notions coincide; moreover, we get genuine pre-well-orderings of axiomatic theories and may drop the non-mathematical quantification over "natural" theories.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
