哥德尔的不完全性定理
Goedel's Incompleteness Theorems hold vacuously
摘要：
在早期的一篇论文中，“在哥德尔的形式系统中的欧米茄不一致：Entscheidungsproblem的建设性证明”（math/0206302），我认为哥德尔推理的建设性解释建立了任何形式的算术系统作为欧米茄不一致。由此可见，哥德尔定理VI是不成立的。本文证明了哥德尔定理11的本质是：如果我们假设存在一个P-公式[Con（P）]，其标准解释等价于断言“P是相容的”，那么[Con（P）]不是P-可证的。我认为没有这样的公式。
英文摘要：
In an earlier paper, "Omega-inconsistency in Goedel's formal system: a constructive proof of the Entscheidungsproblem" (math/0206302), I argued that a constructive interpretation of Goedel's reasoning establishes any formal system of Arithmetic as omega-inconsistent. It follows from this that Goedel's Theorem VI holds vacuously. In this paper I show that Goedel's Theorem XI essentially states that, if we assume there is a P-formula [Con(P)] whose standard interpretation is equivalent to the assertion "P is consistent", then [Con(P)] is not P-provable. I argue that there is no such formula.
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