Gödel incompleteness, graduate course, Notre Dame, Fall 2024

This will be a graduate course at the University of Notre Dame.

Course title: Gödel incompleteness

Course description. We shall explore at length all aspects of the Gödel incompleteness phenomenon, covering Turing’s solution of the Entsheidungsproblem, Gödel’s argument via fixed points, arithmetization, the Hilbert program, Tarski’s theorem, Tarski via Gödel, Tarski via Russell, Tarski via Cantor, the non-collapse of the arithmetic hierarchy, Löb’s theorem, the second incompletenesss theorem via Gödel, via Grelling-Nelson, via Berry’s paradox, Smullyan incompleteness, self-reference, Kleene recursion theorem, Quines, the universal algorithm, and much more. The course will follow the gentle treatment of my book-in-progress, Ten proofs of Gödel incompleteness, with supplemental readings.