关于范畴算术的一个常见误解
A common Misconception about the Categorical Arithmetic
摘要：
虽然范畴算术不能有效地公理化，但不完全性定理可以应用于它的信念相当普遍。此外，可以由这些定理推导出的二阶逻辑的所谓“本质”（或“固有”）语义不完备性并不意味着可以使用Loewenheim-Skolem或紧致性定理推导出的标准语义不完备性。这种状况起源于1930年柯尼斯堡大会上对哥德尔的一个不正确和误解的评论，并由于不同的情况而得到巩固。本文旨在澄清这些问题，并提出了另一种解释的哥德尔的声明。
英文摘要：
Although the categorical arithmetic is not effectively axiomatizable, the belief that the incompleteness Theorems can be apply to it is fairly common. Furthermore, the so-called "essential" (or "inherent") semantic incompleteness of the second-order Logic that can be deduced by these same Theorems does not imply the standard semantic incompleteness that can be derived using the Loewenheim-Skolem or the compactness Theorem. This state of affairs has its origins in an incorrect and misinterpreted Goedel's comment at the Koenigsberg congress of 1930 and has consolidated due to different circumstances. This paper aims to clear up these questions and proposes an alternative interpretation for the Goedel's statement.
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。
