Cours : Natacha Portier
TD : Guilhem Gamard & Alexis Ghyselen
Naive set theory :
- Set theory, Cantor-Bernstein.
- Ordinals, cardinals, well quasi order, Veblen hierarchy.
- Axiom of choice.
First order theories :
- First order languages, natural deduction.
- First order theory, and extensions.
- Peano Arithmetics (PA), Zermelo-Fraenkel Set Theory (ZF).
Tarski’s models :
- Structures and isomorphisms
- Completeness, compactness, Löwenheim-Skolem theorems.
- Applications to PA and ZF.
Incompleteness theorems :
- Undecidability of arithmetics, link with recursive functions.
- Gödel’s incompleteness theorems.