 | Study programme 2021-2022 | Français | |
 | Model theory I | ||
Programme component of Bachelor's in Mathematics à la Faculty of Science |
| Code | Type | Head of UE | Department’s contact details | Teacher(s) |
|---|---|---|---|---|
| US-B3-SCMATH-009-M | Compulsory UE | POINT Françoise | S838 - Logique mathématique |
|
| Language of instruction | Language of assessment | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Credits | Weighting | Term |
|---|---|---|---|---|---|---|---|---|---|
| Français | 15 | 15 | 0 | 0 | 0 | 4 | 4.00 | 2nd term |
| AA Code | Teaching Activity (AA) | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Term | Weighting |
|---|---|---|---|---|---|---|---|---|
| S-MATH-023 | Model Theory I | 15 | 15 | 0 | 0 | 0 | Q2 | 100.00% |
| Programme component |
|---|
Objectives of Programme's Learning Outcomes
- Understand "elementary" mathematics profoundly
- Understand and use the naive set theory
- Understand basic algebraic structures
- Manipulate previously acquired knowledge that appears in a question
- Give examples and counterexamples for definitions, properties, theorems, etc.
- Understand and produce strict mathematical reasoning
- Write clearly and concisely
- Use mathematical vocabulary and formalism appropriately
- Make sense of formal expressions
- Collaborate on mathematical subjects
- Present mathematical results orally and in a structured manner
- Solve new problems
- Abstract and manipulate theories and use these to solve problems
- Use knowledge from different fields to address issues
- Address literature and interact within other scientific fields
- Have sufficient knowledge of English in order to read and understand scientific texts, especially in the field of mathematics.
Learning Outcomes of UE
Be comfortable with the basic notions of Model Theory and with solving simple exercices.
Content of UE
Lowenheim-Skolem theorems, elementary substructures, existentially closed ones. Model-complete theories, quantifier elimination (criteria for these properties). Algebraic examples for these notions. Back-and-forth and dense/discrete orders. Equivalence relations. Introduction to the notion of types. Categoricity and Ryll-Nardweski theorem.
Prior Experience
It relies on the first course on logic and model theory given by Christian Michaux.
Type of Assessment for UE in Q1
- Written examination
Q1 UE Assessment Comments
The evaluation consists in a written exam.
Type of Assessment for UE in Q2
- Written examination
Q2 UE Assessment Comments
evaluation during the semester which is taken into account on the final evaluation.
Type of Assessment for UE in Q3
- Written examination
Q3 UE Assessment Comments
The evaluation consists in a written exam on exercices and a theoretical knowledge of the material.
Type of Resit Assessment for UE in Q1 (BAB1)
- Written examination
Q1 UE Resit Assessment Comments (BAB1)
Not applicable
Type of Teaching Activity/Activities
| AA | Type of Teaching Activity/Activities |
|---|---|
| S-MATH-023 |
|
Mode of delivery
| AA | Mode of delivery |
|---|---|
| S-MATH-023 |
|
Required Reading
| AA | Required Reading |
|---|---|
| S-MATH-023 | Note de cours - Théorie des modèles 1 - Francoise Point |
Required Learning Resources/Tools
| AA | Required Learning Resources/Tools |
|---|---|
| S-MATH-023 | Marker, D., Model theory. An introduction. Graduate Texts in Mathematics, 217. Springer-Verlag, New York, 2002. Chang, C. C.; Keisler, H. J. Model theory. Third edition. Studies in Logic and the Foundations of Mathematics, 73. North-Holland Publishing Co., Amsterdam, 1990, 1977, 1973. |
Recommended Reading
| AA | |
|---|---|
| S-MATH-023 |
Recommended Learning Resources/Tools
| AA | Recommended Learning Resources/Tools |
|---|---|
| S-MATH-023 | Not applicable |
Other Recommended Reading
| AA | Other Recommended Reading |
|---|---|
| S-MATH-023 | Poizat B., Cours de théorie des modèles, 1985, Nur Al-Mantiq Wal-Ma'rifah. [Version anglaise éditée chez Springer en 2000.] Hodges, W., Model theory. Encyclopedia of Mathematics and its Applications, 42. Cambridge University Press, Cambridge, 1993. |
Grade Deferrals of AAs from one year to the next
| AA | Grade Deferrals of AAs from one year to the next |
|---|---|
| S-MATH-023 | Authorized |