Advanced Mathematical Logic: Model Theory (V4A7)

Lecturers

• Dr. Philipp Lücke
• Dr. Philipp Schlicht

Time and Date

• Lecture: Tuesday 10.15 - 12.00 and Thursday 8.15-10.00, seminar room 0.011 (there was an additional lecture on Wednesday 8.11. 10.15-12.00)
• Tutorial: Monday 9.30-11.00, seminar room 0.011, Andreas Lietz

We ask that you get at least around 50% of the points in the exercises to be admitted to the final oral exam. It's ok to submit the solutions in groups of two, only if you cannot find a partner in groups of three.

Contents

Model theory studies classes of models of a first-order theory, for instance groups, fields and graphs, and their abstract properties. An example of such a property is categoricity in a cardinal - the condition that there is exactly one model of this size up to isomorphism. We will study various topics in model theory - possible topics include quantifier elimination, types, categorical theories, Morley’s theorem, stability theory. Model theory is strongly connected with and motivated by algebraic examples, which we will study in the lecture. The following lecture notes might contain mistakes.

• Lecture notes

Literature: Tent, Ziegler - A Course in Model Theory. Marker - Model theory: An Introduction.

Problem sheets

• Problem set 1
• Problem set 2
• Problem set 3
• Problem set 4
• Problem set 5
• Problem set 6
• Problem set 7
• Problem set 8
• Problem set 9
• Problem set 10
• Problem set 11

Exams

The oral exams will take place on Thursday 1.2. and Friday 2.2.2018. The second oral exams will take place on Monday 19.3. and Tuesday 20.3.2018.