Goedel形式系统中的Omega-不一致性：判定问题的构造性证明
Omega-inconsistency in Goedel's formal system: a constructive proof of the Entscheidungsproblem
摘要：
如果我们将演绎元定理推广到哥德尔的“不可判定性”元推理中，我们可以得出结论，哥德尔的算术形式系统不是ω-相容的。如果我们把PA公式[（Ax）F（x）]的标准解释“（Ax）（F（x）”理解为“有一个一般的、x独立的例程来建立F（x）对所有x成立”，而不是“F（x）对所有x成立”，那么可以得出，一个构造性解释的ω-不一致系统否定地证明了希尔伯特的判定问题。
英文摘要：
If we apply an extension of the Deduction meta-Theorem to Goedel's meta-reasoning of "undecidability", we can conclude that Goedel's formal system of Arithmetic is not omega-consistent. If we then take the standard interpretation "(Ax)(F(x)" of the PA-formula [(Ax)F(x)] to mean "There is a general, x-independent, routine to establish that F(x) holds for all x", instead of "F(x) holds for all x", it follows that a constructively interpreted omega-inconsistent system proves Hilbert's Entscheidungsproblem negatively.
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