How definitive is the standard interpretation of Goedel's Incompleteness Theorem?

Mathematics – General Mathematics

Scientific paper

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Scientific paper

Standard interpretations of Goedel's "undecidable" proposition, [(Ax)R(x)],
argue that, although [~(Ax)R(x)] is PA-provable if [(Ax)R(x)] is PA-provable,
we may not conclude from this that [~(Ax)R(x)] is PA-provable. We show that
such interpretations are inconsistent with a standard Deduction Theorem of
first order theories.

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