This page links to the 2014 version of notes originally written to accompany short lecture courses given at Cambridge and at the University of Canterbury at Christchurch NZ in 2010-11. The updating of the notes to a new edition is currently work in progress, but there is now a first complete draft.
These notes aimed to fill the gap between what can be covered in pretty relaxed chalk-and-talk lectures on the one hand and my not-so-very-introductory Introduction to Gödel’s Theorems on the other. However, I’ve tried to make them reasonably stand-alone. The series is encouragingly entitled ‘Gödel Without (Too Many) Tears’.
Here are the current titles of the now twelve episodes [the old fourth one has become two]:
- Incompleteness — The Very Idea
- Incompleteness and undecidability
- Two weak arithmetics
- First-order Peano Arithmetic
- Quantifier complexity
- Primitive recursive functions
- Expressing and capturing the primitive recursive functions
- The arithmetization of syntax
- The first incompleteness theorem
- The Diagonalization Lemma, Rosser and Tarski
- Introducing the Second Theorem
- Curry’s Paradox, Löb’s Theorem and other excitements
(Last updated, February 20, 2014.)