Reviewing Goedel's and Rosser's meta-reasoning of undecidability

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dc.creatorAnand, Bhupinder Singh
dc.date2002-04-16
dc.date2003-05-11
dc.date.accessioned2026-07-07T04:47:44Z
dc.date.available2026-07-07T04:47:44Z
dc.descriptionI review the classical conclusions drawn from Goedel's meta-reasoning establishing an undecidable proposition GUS in standard PA. I argue that, for any given set of numerical values of its free variables, every recursive arithmetical relation can be expressed in PA by different, but formally equivalent, propositions. This asymmetry yields alternative Representation and Self-reference meta-Lemmas. I argue that Goedel's meta-reasoning can thus be expressed avoiding any appeal to the truth of propositions in the standard interpretation IA of PA. This now establishes GUS as decidable, and PA as omega-inconsistent. I argue further that Rosser's extension of Goedel's meta-reasoning involves an invalid deduction.
dc.descriptionv3: Introduced ACI compliant notation for citations. 30 pages. An HTML version is available on the web at http://alixcomsi.com/index01.htm
dc.identifierhttps://arxiv.org/abs/math/0204199
dc.identifierhttp://arxiv.org/abs/math/0204199
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63830
dc.subjectGeneral Mathematics
dc.subject03B10
dc.titleReviewing Goedel's and Rosser's meta-reasoning of undecidability
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