Study programme 2018-2019 | Français | ||
Model Theory II Project | |||
Activité d'apprentissage à la Faculty of Science |
Code | Lecturer(s) | Associate Lecturer(s) | Subsitute Lecturer(s) et other(s) |
---|---|---|---|
S-MATH-050 |
|
Language of instruction | Language of assessment | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Term |
---|---|---|---|---|---|---|---|
Français | Français | 15 | 0 | 45 | 0 | 0 | A |
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
Type of Teaching Activity/Activities
Evaluations
The assessment methods of the Learning Activity (AA) are specified in the course description of the corresponding Educational Component (UE)