2002/07/09 by Bhupinder Singh Anand, Anand, Bhupinder Singh
Computer Science · Mathematics · #03B10 #Advanced Algebra and Logic #FOS: Mathematics #General Mathematics (math.GM) #math.GM #msc:03B10
paper · pdf · doi:10.48550/arxiv.math/0207080
v2. Introduced ACI compliant notation for citations. 9 pages. An HTML version is available at http://alixcomsi.com/index01.htm
openalex publication_date 2002/07/09 · arxiv created 2003/05/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.