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

Syllabus

  • Ultraproducts, compactness.
  • Elementary extensions, Lowenheim-Skolem theorems.
  • Diagram method, preservation theorems.
  • Back-and-forth arguments, elimination of quantifiers.
  • The space of types, omitting types theorem, kappa-saturated models, atomic models.
  • Omega-categorical theories, Ryll-Nardzewski's theorem. Decidability of some axiomatic theories.

Bibliography

  • C.C. CHANG & H.J. KEISLER, Model Theory, North-Holland, 1990.
  • R. CORI & D. LASCAR, Logique mathématique : cours et exercices, Dunod, 2 tomes, 2003.
  • W. HODGES, Model Theory, Cambridge University Press, 1993.
  • D. MARKER, Model theory, An introduction, Graduate Texts in Mathematics, 217, Springer- Verlag, New York, 2002.
  • B. POIZAT, Cours de Théorie des Modèles, Nur al-Mantiq wal-Ma’rifah, 1985. [Version anglaise éditée chez Springer en 2000.]
  • K. TENT & M. ZIEGLER, A Course in Model Theory. Lecture Notes in Logic, Cambridge University.