Model Theory II Project

		Study programme 2019-2020	Français
		Model Theory II Project
		Learning Activity

Code	Lecturer(s)	Associate Lecturer(s)	Subsitute Lecturer(s) et other(s)	Establishment
S-MATH-050			POINT Françoise	Université de Mons

Language of instruction	Language of assessment	HT(*)	HTPE(*)	HTPS(*)	HR(*)	HD(*)	Term
Français	Français	15	0	45	0	0	A

Organisational online arrangements for the end of Q3 2019-2020 assessments (Covid-19)
Oral exam (questions and answers, presentation of individual or group work, comment and argument about a written text...) Production of individual or group work, essay, report, dissertation...
Description of the modifications to the Q3 2019-2020 online assessment procedures (Covid-19)
The material was the book of Pierre Simon on NIP theories (Lecture Notes in Logic 2015) together with notes of Artem Chernikov. At the end of the first semester, a first evaluation consisted in an oral presentation by the student of the quantifier elimination result on Presburger arithmetic (not a matrial covered by the course). A second evaluation consisted of the presentation of aresult of R. Buchi on the decidability of monadic second-order theory of the natural numbers with the successor -written notes (18 pages), together with an oral presenation to the model theory seminar (two lectures and an half)-also a material not covered in class. A third evaluation consisted in the presentation of a choice of results in the course material together with written notes.

Content of Learning Activity

The aim of the course is to understand the proof of Morley's Theorem on aleph_1-categorical theories.
We begin by Ryll-Nardewski's Theorem on aleph_0-categorical theories. Then we will study the following notions:
-saturation, indiscernible sequences.
-Ramsey theorem and Ehrenfeucht-Mostwski's models.
-Vaught pairs, strongly minimal sets and pregeometries.
Finally of time permits:
- Morley and Cantor-Bendixon's ranks.
- definable types, heirs and co-heirs. Application in theories of modules.
- Fraïssé limits (e.g. the random graph).

Required Learning Resources/Tools

Marker, David Model theory. An introduction. Graduate Texts in Mathematics, 217. Springer-Verlag, New York, 2002.

Tent K., Ziegler M., A course in Model Theory, Lecture Notes in Logic, Cambridge University Press, 2012.

Recommended Learning Resources/Tools

Poizat B., Cours de th\'eorie des mod\`eles, 1985, Nur Al-Mantiq Wal-Ma'rifah. [Version anglaise éditée chez Springer en 2000.]

Hodges, Wilfrid Model theory. Encyclopedia of Mathematics and its Applications, 42. Cambridge University Press, Cambridge, 1993.