The main course: • The ω-rule • Induction: the induction axiom, the induction rule, the induction schema • First-order Peano Arithmetic • Why we might have expected PA to be negation complete Dessert: • The idea of ∆0, Σ1, and Π1 wffs • Addendum: A consistent extension of Q is sound for Π1 wffs This episode, after the preamble, falls into two parts. First I introduce the canonical first-order theory of arithmetic, PA. Then – tacked on here, because I need to fit it in somewhere soon and this is as good a place as any – I introduce some terminology for distinguishing wffs on the basis of their ‘quantifier complexity’. Do make sure you understand the idea of induction, and how that is handled in PA, before reading the rest of the episode.