Study programme 2022-2023 | Français | ||
Model Theory II Project (List A) | |||
Programme component of Master's in Mathematics (MONS) (day schedule) à la Faculty of Science |
Code | Type | Head of UE | Department’s contact details | Teacher(s) |
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US-M1-SCMATH-008-M | Optional UE | POINT Françoise | S838 - Logique mathématique |
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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 |
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S-MATH-050 | Model Theory II Project | 15 | 0 | 45 | 0 | 0 | A | 100.00% |
Programme component |
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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, Springer-Verlag, New York, 2002).
UE Content: description and pedagogical relevance
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 Teaching Activity/Activities
AA | Type of Teaching Activity/Activities |
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S-MATH-050 |
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Required Learning Resources/Tools
AA | Required Learning Resources/Tools |
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S-MATH-050 | 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
AA | Recommended Learning Resources/Tools |
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S-MATH-050 | 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
AA | Other Recommended Reading |
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S-MATH-050 | 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 |
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S-MATH-050 | Authorized |
Term 1 Assessment - comments
AA | Term 1 Assessment - comments |
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S-MATH-050 | Not applicable |
Term 2 Assessment - comments
AA | Term 2 Assessment - comments |
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S-MATH-050 | Not applicable |
Term 3 Assessment - comments
AA | Term 3 Assessment - comments |
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S-MATH-050 | Not applicable |