Content of Learning Activity

The aim of the course is to understand the proof of Morley's Theorem on aleph_1-categorical theories.
We begin by Ryll-Nardewski's Theorem on  aleph_0-categorical theories. Then we will study the following notions:
-saturation, indiscernible sequences.
-Ramsey theorem and Ehrenfeucht-Mostwski's models.
-Vaught pairs, strongly minimal sets and pregeometries.
Finally of time permits:
- Morley and Cantor-Bendixon's ranks.
-  definable types, heirs and co-heirs. Application in theories of modules.
- Fraïssé limits (e.g. the random graph).

Required Learning Resources/Tools

Marker, David 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.
 

Recommended Learning Resources/Tools

Poizat B., Cours de th\'eorie des mod\`eles, 1985, Nur Al-Mantiq Wal-Ma'rifah. [Version anglaise éditée chez Springer en 2000.]

Hodges, Wilfrid Model theory. Encyclopedia of Mathematics and its Applications, 42. Cambridge University Press, Cambridge, 1993.

Other Recommended Reading

Jacobson, N., Basic Algebra 2, W.H. Freeman and Compagny, San Francisco, 1980.

 Pillay A.,  An introduction to stability theory, Clarendon Press, Oxford, 1983. [Autre édition: Dover].
 

Mode of delivery

• Face to face

Type of Teaching Activity/Activities

• Cours magistraux
• Conférences
• Préparations, travaux, recherches d'information

Evaluations

The assessment methods of the Learning Activity (AA) are specified in the course description of the corresponding Educational Component (UE)