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

Abstract

I 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.