Study programme 2021-2022Français
Model Theory II Project (List A)
Programme component of Master's in Mathematics à la Faculty of Science

CodeTypeHead of UE Department’s
contact details
Teacher(s)
US-M1-SCMATH-008-MOptional UEPOINT FrançoiseS838 - Logique mathématique
  • POINT Françoise

Language
of instruction
Language
of assessment
HT(*) HTPE(*) HTPS(*) HR(*) HD(*) CreditsWeighting Term
  • Français
Français150450066.00Full academic year

AA CodeTeaching Activity (AA) HT(*) HTPE(*) HTPS(*) HR(*) HD(*) Term Weighting
S-MATH-050Model Theory II Project1504500A100.00%
Programme component

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 this year during the  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

Not applicable

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

Type of Teaching Activity/Activities

AAType of Teaching Activity/Activities
S-MATH-050
  • Cours magistraux
  • Conférences
  • Préparations, travaux, recherches d'information

Mode of delivery

AAMode of delivery
S-MATH-050
  • Face to face

Required Reading

AA
S-MATH-050

Required Learning Resources/Tools

AARequired Learning Resources/Tools
S-MATH-050Marker, 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 Reading

AA
S-MATH-050

Recommended Learning Resources/Tools

AARecommended Learning Resources/Tools
S-MATH-050Poizat 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

AAOther Recommended Reading
S-MATH-050Jacobson, 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

AAGrade Deferrals of AAs from one year to the next
S-MATH-050Authorized
(*) HT : Hours of theory - HTPE : Hours of in-class exercices - HTPS : hours of practical work - HD : HMiscellaneous time - HR : Hours of remedial classes. - Per. (Period), Y=Year, Q1=1st term et Q2=2nd term
Date de génération : 01/10/2021
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