Study programme 2020-2021Français
Model theory I
Programme component of Bachelor's in Mathematics à la Faculty of Science

Students are asked to consult the ECTS course descriptions for each learning activity (AA) to know what special Covid-19 assessment methods are possibly planned for the end of Q3

CodeTypeHead of UE Department’s
contact details
US-B3-SCMATH-009-MCompulsory UEPOINT FrançoiseS838 - Logique mathématique
  • POINT Françoise

of instruction
of assessment
HT(*) HTPE(*) HTPS(*) HR(*) HD(*) CreditsWeighting Term
  • Français
Français151500044.002nd term

AA CodeTeaching Activity (AA) HT(*) HTPE(*) HTPS(*) HR(*) HD(*) Term Weighting
S-MATH-023Model Theory I1515000Q2100.00%
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
  • Graded tests

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

AAType of Teaching Activity/Activities
  • Cours magistraux
  • Exercices dirigés
  • Démonstrations

Mode of delivery

AAMode of delivery
  • Face to face

Required Reading


Required Learning Resources/Tools

AARequired Learning Resources/Tools
S-MATH-023Marker, 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


Recommended Learning Resources/Tools

AARecommended Learning Resources/Tools
S-MATH-023Not applicable

Other Recommended Reading

AAOther Recommended Reading
S-MATH-023Poizat 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

AAGrade Deferrals of AAs from one year to the next
(*) 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 : 09/07/2021
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