This page links to a new series of handouts for a short course first given in February and March 2010 as a visiting Erskine Fellow at the University of Canterbury at Christchurch NZ, and then revised and extended for a lecture course in Cambridge starting in October 2010 (seven lectures in Michaelmas term, and another four in Lent).
These handouts aim to fill the gap between pretty relaxed chalk-and-talk lectures on the one hand and my not-so-very-introductory Introduction to Gödel’s Theorems on the other. The series is encouragingly entitled ‘Gödel Without (Too Many) Tears’, and updates/somewhat extends previous versions published on this page.
- Incompleteness — The Very Idea
- Incompleteness and undecidability
- Two weak arithmetics
- First-order Peano Arithmetic
- 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
The complete set of handouts can be downloaded here. (Last updated, February 8th, 2011. For ease of maintenance, I’ve now taken down the links to individual episodes as separate files.)