- What to read before, after, or instead of IGT.
- Introductory reading list on Computable Functions. Perhaps useful if you want to pursue this particular topic in detail beyond the very limited treatment in IGT.
Here are notes for three different courses of lectures, at different levels:
- Gödel Without (Too Many) Tears — The 2014 edition of 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
- Expounding the First Theorem — extensive (though far from completed) notes on the expository tradition. Version 2: From 1931 to 1953.
- 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).