Goedel's Incompleteness Theorems hold vacuously
| dc.creator | Anand, Bhupinder Singh | |
| dc.date | 2002-07-09 | |
| dc.date | 2003-05-11 | |
| dc.date.accessioned | 2026-07-07T04:49:36Z | |
| dc.date.available | 2026-07-07T04:49:36Z | |
| dc.description | 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. | |
| dc.description | v2. Introduced ACI compliant notation for citations. 9 pages. An HTML version is available at http://alixcomsi.com/index01.htm | |
| dc.identifier | https://arxiv.org/abs/math/0207080 | |
| dc.identifier | http://arxiv.org/abs/math/0207080 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64484 | |
| dc.subject | General Mathematics | |
| dc.subject | 03B10 | |
| dc.title | Goedel's Incompleteness Theorems hold vacuously | |
| dc.type | text |