Lecture Notes
Here are notes for three different courses of lectures, at different levels:
- Gödel Without (Too Many) Tears — Extensive notes for a short course given to undergraduate philosophers, 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 my last lecture course in Cambridge 2010-2011.
- Lectures on the First Incompleteness Theorem — just four introductory lectures given in Easter term 2011 as a supplement to Thomas Forster’s earlier Part III Maths course on Computable Function Theory. (The first three don’t require any background in the theory of computation over an above a grip on the idea of a primitive recursive function and the idea of coding: only the fourth appeals to results like the unsolvability of the halting problem.)
- Back to Basics: Revisiting the Incompleteness Theorems. The notes for a three-lecture series given to mathematicians at a Cambridge weekend workshop for graduates in 2009. They complement the book by approaching things in a rather different order.
Other relevant handouts
- Induction, More or Less: On Some Subystems of Second-Order Arithmetic. Explains, inter alia, more about ACA0, the theory mentioned in Sec. 22.7.
- Isaacson’s Thesis and Ancestral Arithmetic. A stand-alone paper (published in Analysis) reworking ideas in IGT.
- Church’s Thesis After 70 Years. Discusses papers in a volume of essays on Church’s Thesis (amplifying some remarks in the final chapter).
- The MRDP Theorem. Introductory discussion of the MRDP Theorem and another route to proving the first incompleteness theorem.
- Tennenbaum’s Theorem. Introductory discussion of Tennenbaum’s Theorem (not so closely tied to issues about incompleteness, perhaps, but still interesting as giving us a key insight about models of PA).
- Introductory reading list on Computable Functions. Perhaps useful if you want to pursue the topic beyond the very limited treatment in IGT.