数学不完备性导致一阶皮亚诺算术：早期历史的修正主义观点
Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early History
摘要：
在《数理逻辑手册》中，拉姆齐定理的巴黎-哈林顿变体被认为是对一阶算术中纯数学不完备性结果的长期“搜索”的第一个结果。本文质疑任何这样的搜索的存在和巴黎哈林顿结果的地位作为第一个数学不完全性结果。事实上，我认为根岑给出了第一个这样的结果，并且古德斯坦以数论形式重申了这个结果。
英文摘要：
In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long 'search' for a purely mathematical incompleteness result in first-order arithmetic. This paper questions the existence of any such search and the status of the Paris-Harrington result as the first mathematical incompleteness result. In fact, I argue that Gentzen gave the first such result, and that it was restated by Goodstein in a number-theoretic form.
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。
