Contents

The aim of the course is to understand the proof of Morley's Theorem on aleph_1-categorical theories. <br />We begin by Ryll-Nardewski's Theorem on  aleph_0-categorical theories. Then we will study the following notions: <br />-saturation, indiscernible sequences.<br />-Ramsey theorem and Ehrenfeucht-Mostwski's models.<br />-Vaught pairs, strongly minimal sets and pregeometries.<br />Finally of time permits:<br />- Morley and Cantor-Bendixon's ranks.<br />-  definable types, heirs and co-heirs. Application in theories of modules.<br />- 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.<br /><br />Tent K., Ziegler M., A course in Model Theory, Lecture Notes in Logic, Cambridge University Press, 2012.<br /><br />

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

Mode of delivery

• Face to face

Term 1 Assessment - type

• N/A

Term 1 Assessment - comments

Not applicable

Term 2 Assessment - type

• Oral Examination

Term 2 Assessment - comments

Not applicable

Term 3 Assessment - type

• Oral examination

Term 3 Assessment - comments

Not applicable

Resit Assessment - Term 1 (B1BA1) - type

• N/A

Resit Assessment - Term 1 (B1BA1) - Comments

Not applicable

Type of Teaching Activity/Activities

• Cours (cours magistraux; conférences)
• Préparations, travaux, recherches d'information