 | Study programme 2020-2021 | Français | |
| Model Theory I | |||
Learning Activity |
| Code | Lecturer(s) | Associate Lecturer(s) | Subsitute Lecturer(s) et other(s) | Establishment |
|---|---|---|---|---|
| S-MATH-023 |
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| Language of instruction | Language of assessment | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Term |
|---|---|---|---|---|---|---|---|
| Français | Français | 15 | 15 | 0 | 0 | 0 | Q2 |
| Organisational online arrangements for the end of Q3 2020-2021 assessments (Covid-19) |
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| Description of the modifications to the Q3 2020-2021 assessment procedures (Covid-19) |
| The written exam consists in solving exercices on the material of the model theory course. In the written support of the course a number of exercices are proposed and some solutons are detailed at the end of the document. Furthermore the students have as many exercices sessions as theoretical ones. (In this period of online sessions, it is quite complicated, unlike the previous years, to evaluate the students during the semester.) The exam will be online (on moodle exam) |
Organisational arrangements for the end of Q2 2020-2021 assessments (Covid-19) online or face-to-face (according to assessment schedule)
- Written exam (multiple choice, open questions)
- Oral exam (questions and answers, presentation of individual or group work, comment and argument about a written text...)
Description of the modifications to the Q2 2020-2021 assessment procedures (Covid-19) online or face-to-face (according to assessment schedule)
The written exam consists in solving exercices on the material of the model theory course. After the written exam there is a short oral exam mainly consisting in reviewing the copy of the student.
In the written support of the course a number of exercices are proposed and some solutons are detailed at the end of the document. Furthermore the students have as many exercices sessions as theoretical ones.
(In this period of online sessions, it is quite complicated, unlike the previous years, to evaluate the students during the semester.)
Content of Learning Activity
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.
Required Learning Resources/Tools
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 Learning Resources/Tools
Not applicable
Other Recommended Reading
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.
Mode of delivery
- Face to face
Type of Teaching Activity/Activities
- Cours magistraux
- Exercices dirigés
- Démonstrations
Evaluations
The assessment methods of the Learning Activity (AA) are specified in the course description of the corresponding Educational Component (UE)