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Omega-inconsistency in Goedel's formal system: a constructive proof of the Entscheidungsproblem

Bhupinder Singh Anand
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Abstract

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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Bhupinder Singh Anand. 2003-05-11. Omega-inconsistency in Goedel's formal system: a constructive proof of the Entscheidungsproblem. https://arxiv.org/abs/math/0206302

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