Archive 2019
Program requirementsexamen
TeacherFrançois Le Maître
Weekly hours 2 h CM , 2 h TD
Years Master Logique et Fondements de l'Informatique

Syllabus

  • ordinals, transfinite recursion;
  • axiom of choice and equivalent statements;
  • arithmetic of infinite cardinals; cofinality, regular and singular cardinals, König's theorem;
  • von Neumann's hierarchy, reflection theorems;
  • filters and ultrafilters, stationary sets in $\omega_1$, Fodor's lemma;
  • well-founded relationships and Mostowski's collapse;
  • some elements of descriptive set theory.

Bibliography

  • Cori, R. et Lascar, D., Logique mathématique : cours et exercices, Dunod, 2003.
  • Hrbacek, K. et Jech, T., Introduction to set theory, Third edition, Marcel Dekker, 1999.
  • Krivine, J.L., Théorie des ensembles, Cassini, 1998.