Bachelor's Degree in Mathematics

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

Code	Type	Head of UE	Department’s contact details	Teacher(s)
US-B3-SCMATH-010-M	Compulsory UE	POINT Francoise	S838 - Logique mathématique	MARIAULE Nathanaël POINT Francoise

Language of instruction	Language of assessment	HT(*)	HTPE(*)	HTPS(*)	HR(*)	HD(*)	Credits	Weighting	Term
Français	Français	15	15	0	0	0	2.00	100.00

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%

Unité d'enseignement

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

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, kappa-categorical theories and Vaught Theorem. Back and Forth and dense linear orders. Quantifier-elimination criteria and applications to algebraically closed fields and real-closed fields. Model-complete theories and Lindström theorem. Stone spaces of types and aleph_0-categorical theories.

Prior Experience

Notions of first-order Logic, of (sub)-structures, morphisms. Compacity Theorem and Completeness Theorem. Ultraproducts and Los Theorem. Some notions of naive set theory (ordinals, cardinals),some notion of topology (basis of open sets, compacity), some notions of algebra ((ordered) groups, (ordered) fields, polynomial rings, Boolean algebras).

Type of Assessment for UE in Q1

Q1 UE Assessment Comments

The evaluation consists in a written exam on exercices (1/3) and is completed by an oral exam (2/3).

Type of Assessment for UE in Q2

Oral Examination
Written examination

Q2 UE Assessment Comments

The evaluation consists in a written exam on exercices (1/3) and is completed by an oral exam (2/3).

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.

Q1 UE Resit Assessment Comments (BAB1)

Not applicable

Type of Teaching Activity/Activities

AA	Type of Teaching Activity/Activities
S-MATH-023	Cours magistraux Conférences Exercices dirigés Utilisation de logiciels Démonstrations

Mode of delivery

AA	Mode of delivery
S-MATH-023	Face to face

Required Reading

AA	Required Reading
S-MATH-023	Note de cours - transparente - Françoise 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.