Louise Hay Logic Seminar
Ryan Carpenter
UIC
A Consistency Proof for PA
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.
Wednesday September 11, 2024 at 2:00 PM in 427 SEO