RequirementsBesides the notions and results of the first semester course, a general mathematical background (at Bachelor's level) will be useful to understand some examples and applications.
Program requirementsexamen
TeacherTomás Ibarlucía
Weekly hours 4 h CM
Years Master Logique et Fondements de l'Informatique

Syllabus

This course is a natural continuation of the first semester Model Theory course. It will seek to understand and classify the models of a given 1st order theory through the types that can be realized or omitted.

Contents

  • Spaces of types.
  • Saturated models, homogeneous models.
  • Type omission theorem.
  • Atomic models, prime models.
  • Omega-categorical theories, Ryll-Nardzewski's theorem.
  • Stable and omega-stable theories. Strongly minimal sets.
  • Indescernible sequences and sets.
  • Kappa-categorical theories. Morley and Baldwin-Lachlan theorems.

Bibliography

  • Marker, D., Model theory, An introduction, Graduate Texts in Mathematics, 217, Springer-Verlag, New York, 2002.
  • Tent K., Ziegler M., A course in Model Theory, Lecture Notes in Logic, Cambridge University Press, 2012.