Slides for Computability and Incompleteness course. A fair warning: the slides differ from what I actually do in the class, and they may contain mistakes. I use them as a prop rather than as a definitive reference point.

• Part 1.
  Diagonalisation method.
  Models of computation: recursive functions, abaci, Turing machines.
  Halting problem.
  
• Part 2.
  Properities of theories.
  Robinson arithmetic: representability of recursive functions.
  Goedel numbering and diagonalisation lemma.
  Undecidability of first order logic (Church).
  Incompleteness of extensions of Robinson arithmetic (Goedel).