Speaker: Jin Wei

Title: Let’s Prove the Consistency of Peano Arithmetic

Abstract: You might look at the title and wonder: wait, didn’t Gödel literally show it is impossible? Still, we are going to prove it anyway; in fact, I will present TWO proofs of consistency of Peano Arithmetic, one famously by Gentzen and another less well-known one by Gödel himself! I will explain the historical motivations, ideas of their theory, and how their proofs are consistent with Gödel’s incompleteness theorem. Along the way, I will also introduce modern proof theory topics, such as ordinal analysis and proof mining, and how they are born from this consistency project. As always, this talk is aiming for general audience and no previous background in logic is required!