Study programme 2023-2024 | Français | ||
Mathematical logic and model theory | |||
Programme component of Bachelor'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-B3-SCMATH-005-M | Compulsory UE | MICHAUX Christian | S838 - Logique mathématique |
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Language of instruction | Language of assessment | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Credits | Weighting | Term |
---|---|---|---|---|---|---|---|---|---|
| Français | 50 | 30 | 0 | 0 | 0 | 7 | 7.00 | Année |
AA Code | Teaching Activity (AA) | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Term | Weighting |
---|---|---|---|---|---|---|---|---|
S-MATH-021 | Mathematical logic I | 35 | 15 | 0 | 0 | 0 | Q1 | |
S-MATH-023 | Model Theory I | 15 | 10 | 0 | 0 | 0 | Q2 | |
S-MATH-019 | Seminar of mathematical logic I | 0 | 5 | 0 | 0 | 0 | Q2 |
Programme component |
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Objectives of Programme's Learning Outcomes
Learning Outcomes of UE
At the end of the instruction, the students will be able to understand the role of model theory in mathematics, and more generally of mathematical logic.
UE Content: description and pedagogical relevance
Reminder of the topics of the course of B2 (seminar of introduction to mathematical logic). Basic elements of model theory (languages,formulas, theories, complete theories, model-complete theories, quantifiers elimination), models build by ultraproducts and their use in mathematics (for example to non standard model of real numbers). Completeness Theorem (without the proof), Compactness Theorem, Los Theorem, Constants'Method, Lowenhein-Skolem Theorem, applications (if possible) to types, algebraically closed and real closed fields...
Prior Experience
Basic notions of mathematcial logic ( similar to the content of the seminar of introduction to mathematical logic) and of algebra, linear algebra and topology.
Type(s) and mode(s) of Q1 UE assessment
Q1 UE Assessment Comments
Only Exercices
Method of calculating the overall mark for the Q1 UE assessment
Mark from the written examination (50% of the final mark)
Type(s) and mode(s) of Q1 UE resit assessment (BAB1)
Q1 UE Resit Assessment Comments (BAB1)
not applicable
Method of calculating the overall mark for the Q1 UE resit assessment
not applicable
Type(s) and mode(s) of Q2 UE assessment
Q2 UE Assessment Comments
Not applicable
Method of calculating the overall mark for the Q2 UE assessment
Global mark based on oral presentation (50% of final mark)
Type(s) and mode(s) of Q3 UE assessment
Q3 UE Assessment Comments
Not applicable
Method of calculating the overall mark for the Q3 UE assessment
Idem Q1 + Q2 in a single evaluation
Type of Teaching Activity/Activities
AA | Type of Teaching Activity/Activities |
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S-MATH-021 |
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S-MATH-023 |
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S-MATH-019 |
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Mode of delivery
AA | Mode of delivery |
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S-MATH-021 |
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S-MATH-023 |
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S-MATH-019 |
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Required Learning Resources/Tools
AA | Required Learning Resources/Tools |
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S-MATH-021 | See the pages on Moodle platform. |
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. |
S-MATH-019 | Not applicable |
Recommended Learning Resources/Tools
AA | Recommended Learning Resources/Tools |
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S-MATH-021 | Marker, D., Model theory. An introduction. Graduate Texts in Mathematics, 217. Springer-Verlag, New York, 2002. |
S-MATH-023 | Not applicable |
S-MATH-019 | Not applicable |
Other Recommended Reading
AA | Other Recommended Reading |
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S-MATH-021 | Chang et Keisler, Model Theory, North-Holland. Barwise, Handbook of mathematical logic, North-Holland. 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. |
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. |
S-MATH-019 | Not applicable |