哥德尔不完全性定理的标准解释有多明确？
How definitive is the standard interpretation of Goedel's Incompleteness Theorem?
摘要：
对哥德尔的“不可判定”命题[（Ax）R（x）]的标准解释认为，尽管[~（Ax）R（x）]是PA可证明的，如果[（Ax）R（x）]是PA可证明的，但我们不能由此得出结论[~（Ax）R（x）]是PA可证明的。我们表明，这样的解释是不符合标准的演绎定理的一阶理论。
英文摘要：
Standard interpretations of Goedel's "undecidable" proposition, [(Ax)R(x)], argue that, although [~(Ax)R(x)] is PA-provable if [(Ax)R(x)] is PA-provable, we may not conclude from this that [~(Ax)R(x)] is PA-provable. We show that such interpretations are inconsistent with a standard Deduction Theorem of first order 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。
