2002/06/28 by Bhupinder Singh Anand, Anand, Bhupinder Singh · 1 citation
Computer Science · Mathematics · #03B10 #Advanced Algebra and Logic #FOS: Mathematics #General Mathematics (math.GM) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #math.GM #msc:03B10
paper · pdf · doi:10.48550/arxiv.math/0206302
v3. Introduced ACI compliant notation for citations. 10 pages. An HTML version is available at http://alixcomsi.com/index01.htm
openalex publication_date 2002/06/28 · arxiv created 2003/05/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.