Gödel Without (Too Many) Tears

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]:

  1. Incompleteness — The Very Idea
  2. Incompleteness and undecidability
  3. Two weak arithmetics
  4. First-order Peano Arithmetic
  5. Quantifier complexity
  6. Primitive recursive functions
  7. Expressing and capturing the primitive recursive functions
  8. The arithmetization of syntax
  9. The first incompleteness theorem
  10. The Diagonalization Lemma, Rosser and Tarski
  11. Introducing the Second Theorem
  12. Curry’s Paradox, Löb’s Theorem and other excitements

The complete set of notes can be downloaded here.

(Last updated, February 20, 2014.)

2 Responses to Gödel Without (Too Many) Tears

  1. Caught two typos:

    Episode 1, section 3, paragraph 8 (p. 6): “promisory” should be “promissory”
    Episode 1, section 8, paragraph 1 (p. 10): “seamantics” should be “semantics”

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