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Goedel's Incompleteness Theorems hold vacuously

Bhupinder Singh Anand
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Abstract

In an earlier paper, "Omega-inconsistency in Goedel's formal system: a constructive proof of the Entscheidungsproblem" (math/0206302), I argued that a constructive interpretation of Goedel's reasoning establishes any formal system of Arithmetic as omega-inconsistent. It follows from this that Goedel's Theorem VI holds vacuously. In this paper I show that Goedel's Theorem XI essentially states that, if we assume there is a P-formula [Con(P)] whose standard interpretation is equivalent to the assertion "P is consistent", then [Con(P)] is not P-provable. I argue that there is no such formula.

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Bhupinder Singh Anand. 2003-05-11. Goedel's Incompleteness Theorems hold vacuously. https://arxiv.org/abs/math/0207080

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