The Provability of Consistency

Abstract: We offer a mathematical proof of consistency for Peano Arithmetic PA formalizable in PA. This result is compatible with Goedel's Second Incompleteness Theorem since our consistency proof does not rely on the representation of consistency as a specific arithmetical formula. Our findings show that formal theories can finitely formalize proofs of certain properties presented as schemes without reducing the presentation of those properties to a single formula. We outline a theory of proving schemes in PA.