Ryan Carpenter : A Consistency Proof for PA

Posted by Ryan Carpenter , part of the Louise Hay Logic Seminar.

At

Sept. 11, 2024, 2 p.m.

In

427 SEO

Abstract

I will attempt to succinctly present a modified version of Gerhard Gentzen's proof of the consistency of PA. This approach is adopted from course notes by Henry Towsner, a contemporary proof-theoricist, so the presentation matches what current research efforts in proof theory look like. In the talk, I will detail a few deduction calculi, prove results on the elimination of certain of their rules for special theories, and show how these results lead toward a consistency proof for Peano Arithmetic. To close, we will consider the proof of the main result in light of Godel's theorems.