  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.
