Study programme 20202021  Français  
Model Theory II Project (List A)  
Programme component of Master's in Mathematics à la Faculty of Science 
Students are asked to consult the ECTS course descriptions for each learning activity (AA) to know what special Covid19 assessment methods are possibly planned for the end of Q3 

Code  Type  Head of UE  Department’s contact details  Teacher(s) 

USM1SCMATH008M  Optional UE  POINT Françoise  S838  Logique mathématique 

Language of instruction  Language of assessment  HT(*)  HTPE(*)  HTPS(*)  HR(*)  HD(*)  Credits  Weighting  Term 

 Français  15  0  45  0  0  6  6.00  Full academic year 
AA Code  Teaching Activity (AA)  HT(*)  HTPE(*)  HTPS(*)  HR(*)  HD(*)  Term  Weighting 

SMATH050  Model Theory II Project  15  0  45  0  0  A  100.00% 
Programme component 

Objectives of Programme's Learning Outcomes
Learning Outcomes of UE
Be able to read the Model theory book of Dave Marker (Model Theory, An introduction, Graduate Texts in Mathematics, 217, SpringerVerlag, New York, 2002).
Content of UE
The aim of the course is to understand the proof of Morley's Theorem on aleph_1categorical theories.
We begin by RyllNardewski's Theorem on aleph_0categorical theories. Then we will study the following notions:
saturation, indiscernible sequences.
Ramsey theorem and EhrenfeuchtMostwski's models.
Vaught pairs, strongly minimal sets and pregeometries.
Finally of time permits:
 Morley and CantorBendixon's ranks.
 definable types, heirs and coheirs. 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
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
Q2 UE Assessment Comments
The evaluation for the Q2 is similar to the one for the Q1.
Type of Assessment for UE in Q3
Q3 UE Assessment Comments
Not applicable
Type of Resit Assessment for UE in Q1 (BAB1)
Q1 UE Resit Assessment Comments (BAB1)
Not applicable
Type of Teaching Activity/Activities
AA  Type of Teaching Activity/Activities 

SMATH050 

Mode of delivery
AA  Mode of delivery 

SMATH050 

Required Reading
AA  

SMATH050 
Required Learning Resources/Tools
AA  Required Learning Resources/Tools 

SMATH050  Marker, David Model theory. An introduction. Graduate Texts in Mathematics, 217. SpringerVerlag, New York, 2002. Tent K., Ziegler M., A course in Model Theory, Lecture Notes in Logic, Cambridge University Press, 2012. 
Recommended Reading
AA  

SMATH050 
Recommended Learning Resources/Tools
AA  Recommended Learning Resources/Tools 

SMATH050  Poizat B., Cours de th\'eorie des mod\`eles, 1985, Nur AlMantiq WalMa'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
AA  Other Recommended Reading 

SMATH050  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]. 
Grade Deferrals of AAs from one year to the next
AA  Grade Deferrals of AAs from one year to the next 

SMATH050  Authorized 