HackerPapers

arXiv:1902.07404math.LO

The Provability of Consistency

Sergei Artemov

Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.

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.

arXiv comments
A compact exposition of the main result and a brief foundational discussion
Journal reference
DOI
Subjects
math.LOLogic

On Hacker News

Linked by 1 identifiable commenter in 1 comment across 1 thread, from Jan 2021 to Jan 2021.

Comments linking this paper, per year.

Discussed in comments1 thread

  1. From Trotsky to Gödel: The Life of Jean van Heijenoort 1 comment

    • Let me try to reconstruct what has been said. You seem to be reacting to points different from the one I tried to make. bjornsing: All of mathematics can in principle be derived from ZFC. morelisp: not all, there are independent statements. Mathematics is beyond formalization.…

      burakemirView on HNParent context

Submitted to Hacker News

Connected through shared HN threads, not inferred similarity or a recommendation.