Objectives of Programme's Learning Outcomes

• Have integrated and elaborate mathematical knowledge.
• Mobilise the Bachelor's course in mathematics to address complex issues and have profound mathematical expertise to complement the knowledge developed in the Bachelor's course.
• Use prior knowledge to independently learn high-level mathematics.
• Research mathematical literature in an efficient and relevant way.
• Read research articles in at least one discipline of mathematics.
• Carry out major projects.
• Independently carry out a major project related to mathematics or mathematical applications. This entails taking into account the complexity of the project, its objectives and the resources available to carry it out.
• Give constructive criticism on the quality and progress of a project.
• Work in teams and, in particular, communicate effectively and with respect for others.
• Appropriately use bibliographic resources for the intended purpose.
• Present the objectives and results of a project orally and in writing.
• Apply innovative methods to solve an unprecedented problem in mathematics or within its applications.
• Mobilise knowledge, and research and analyse various information sources to propose innovative solutions targeted unprecedented issues.
• Communicate clearly.
• make a structured and reasoned presentation of the content and principles underlying a piece of work, mobilised skills and the conclusions it leads to.

Learning Outcomes of UE

Be able to read the Model theory book of Dave Marker (Model Theory, An introduction, Graduate Texts in Mathematics, 217, Springer-Verlag, New York, 2002).

Content of UE

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).

Prior Experience

This course follows the model theory course 1, given in Bac 3.

Type of Assessment for UE in Q1

• Presentation and/or works
• Oral examination

Q1 UE Assessment Comments

This course is taught both during the Q1 and Q2 and the program adapts to the requirements of the students present. (This comment referes to the description given above which is suited to students who would continue in model theory).

Type of Assessment for UE in Q2

• Presentation and/or works
• Oral Examination

Q2 UE Assessment Comments

The evaluation for the Q2 is similar to the one for the Q1.

Type of Assessment for UE in Q3

• Oral examination

Q3 UE Assessment Comments

Not applicable

Type of Resit Assessment for UE in Q1 (BAB1)

• Oral examination

Q1 UE Resit Assessment Comments (BAB1)

Not applicable