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

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

2002-06-28

arxiv.org/abs/math/0206302v2

Mathematics

General Mathematics

v3. Introduced ACI compliant notation for citations. 10 pages. An HTML version is available at http://alixcomsi.com/index01.ht

Scientific paper

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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