Goedel's Incompleteness Theorems hold vacuously
综合数学
2007-05-23 v2
摘要
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.
引用
@article{arxiv.math/0207080,
title = {Goedel's Incompleteness Theorems hold vacuously},
author = {Bhupinder Singh Anand},
journal= {arXiv preprint arXiv:math/0207080},
year = {2007}
}
备注
v2. Introduced ACI compliant notation for citations. 9 pages. An HTML version is available at http://alixcomsi.com/index01.htm