LOG – Mathematical logics (2nd semester, 6 ECTS)

Alexandre Miquel

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.