Five Conferences on Undecidability

Nicolas Bouleau (1) , Jean-Yves Girard (2) , Alain Louveau (3)

1 CIRED - centre international de recherche sur l'environnement et le développement
2 IML - Institut de mathématiques de Luminy
3 IMJ - Institut de Mathématiques de Jussieu

These five lectures on undecidability were given to students with a good level in mathematics but with no special knowledge on logic. The first conference presents the formalization of mathematics with a short historical survey, the language of first order predicates and the axioms of set theory. The second and third lectures explain the incompleteness phenomena from the Hilbert program until Gödel's theorems with a presentation of the sequent calculus of Gentzen.The fourth talk deepens model theory reasoning in the case of the continuum hypothesis, and the last conference gives examples of effective computability results.

Mots clés: undecidability; set theory; predicate; logic; Hilbert program; incompleteness; consistency; recursive function; sequent; ordinal; cardinal; continuum; algorithm

Domaines: Logique [math.LO]

Nicolas Bouleau, Jean-Yves Girard, Alain Louveau. Five Conferences on Undecidability. N. Bouleau. Presses de l'Ecole Nationale des Ponts et Chaussées, pp.57, 1983. ⟨hal-00192557⟩